In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilin...In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.展开更多
In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the...In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.展开更多
Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing ...Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.展开更多
Most existing 2-dimensional barcodes are designed with a fixed shape and clear area.Having a fixed shape and clear area makes the barcode difficult to lay out with other text and pictures.To solve this problem,an amor...Most existing 2-dimensional barcodes are designed with a fixed shape and clear area.Having a fixed shape and clear area makes the barcode difficult to lay out with other text and pictures.To solve this problem,an amorphous 2-dimensional barcode is presented in this paper.The barcode uses encoding graph units to encode data.There are two key points in a 2-dimensional barcode:One is the encoding graph unit,the other is its encoding rules.Because encoding graph units of a 2-dimensional barcode are surrounded by other graphics,the units should be self-positioned and distinguished from other units.This paper presents an encoding graph unit generation algorithm,which is based on genetic algorithms.Encoding rules of the barcode are also given in this paper.Those rules include data encoding rules and encoding graph unit sequence arrangement rules.Data encoding rules are used to encode data to an encoding graph unit sequence.Encoding graph unit sequence arrangement rules are used to embed the unit sequence in the target picture.In addition to those rules,it also discussed the steps to restore encoding graph unit sequence from a picture.In the experiments section of this paper,an example is provided to encode a string and embed it in a car ad picture by the barcode.According to encoding rules of the barcode,those encoding graphic units can be scattered and embedded in a picture with other graphics,so amorphous 2-dimensional barcode has no fixed shape.Take advantage of this,designer can present a more elegant design to lay out barcodes with other graphic elements.展开更多
We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads ...We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.展开更多
The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryf...The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.展开更多
BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and sev...BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and severe PPH, any dramatic hemodynamic changes in liver transplantation or other procedures may result in death from pulmonary and cardiac events. In this study, we investigated the prevalence of PPH in patients with portal hypertension (PHT) mainly caused by hepatitis B virus, and evaluated the effect of 2-dimensional Doppler echocardiography (2D-ECHO) in screening for PPH. METHODS: One hundred and five PHT patients received transthoracic 2D-ECHO preoperatively, systolic pulmonary arterial pressure (SPAP, normal range <30 mmHg) and pulmonary acceleration time (PAT, normal range >= 120 msec) were measured to screen for PPH (positive result: SPAP >= 30 mmHg and/or PAT <100 msec). Subsequently, pulmonary hemodynamic parameters were measured by right heart catheterization (RHC) for definitive diagnosis of PPH. The results of the two methods were compared to assess the screening effect of 2D-ECHO. RESULTS: The prevalence of PPH in this study was 3.8% (4/105). About 90% (95/105) of patients had a detectable tricuspid regurgitation by 2D-ECHO and the mean SPAP was 27.7 +/- 5.9 mmHg. Twenty-two of these 95 patients had an SPAP >30 mmHg. The mean PAT of all patients was 140 23 msec and 5 were <100 msec. Twenty-two patients were screened out by 2D-ECHO and 4 were diagnosed by RHC. A positive significant correlation (r=0.55, P<0.01) was found between SPAP measured by 2D-ECHO and mean pulmonary artery pressure (MPAP) measured by RHC, and a weak but significant negative correlation (r=-0.27, P=0.005) existed between PAT and pulmonary vascular resistance (PVR). The sensitivity, specificity, agreement rate, positive predictive value and negative predictive value of the screening test were 100%, 82%, 83%, 18% and 100%, respectively. CONCLUSIONS: The prevalence of PPH in this study is lower than in Western countries. As a screening test, 2D-ECHO has very high sensitivity and negative predictive value. A negative test result can directly be used to exclude PPH, while a positive result should be confirmed by RHC.展开更多
Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.u...Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.展开更多
In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational lo...In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the(2+1)-dimensional Sawada–Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions.展开更多
In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and othe...In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.展开更多
A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic w...A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.展开更多
New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solu...New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.展开更多
In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equati...In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.展开更多
The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–D...The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.展开更多
Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method...Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.展开更多
In this paper,based on N-soliton solutions,we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in(2+1)-dimensional integrable systems.Then,we take the(2+1)-dimensional Sawada...In this paper,based on N-soliton solutions,we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in(2+1)-dimensional integrable systems.Then,we take the(2+1)-dimensional Sawada–Kotera equation as an example to illustrate how to generate these resonance Y-type soliton solutions with this new constraint.Next,by the long wave limit method,velocity resonance and module resonance,we can obtain some new types of hybrid solutions of resonance Y-type solitons with line waves,breather waves,high-order lump waves respectively.Finally,we also study the dynamics of these interaction solutions and indicate mathematically that these interactions are elastic.展开更多
In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple dire...In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem.展开更多
Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic so...Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.展开更多
Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechan...Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.展开更多
In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian s...In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian solutions have been generated.展开更多
基金supported by the National Natural Science Foundation of China,Grant No.12375006。
文摘In this paper,we investigate the(2+1)-dimensional three-component long-wave-short-wave resonance interaction system,which describes complex systems and nonlinear wave phenomena in physics.By employing the Hirota bilinear method,we derive the general nondegenerate N-soliton solution of the system,where each short-wave component contains N arbitrary functions of the independent variable y.The presence of these arbitrary functions in the analytical solution enables the construction of a wide range of nondegenerate soliton types.Finally,we illustrate the structural features of several novel nondegenerate solitons,including M-shaped,multiple double-hump,and sawtooth double-striped solitons,as well as interactions between nondegenerate solitons,such as dromion-like solitons and solitoffs,with the aid of figures.
基金supported by the National Natural Science Foundation of China(12371255,11975306)the Xuzhou Basic Research Program Project(KC23048)+1 种基金the Six Talent Peaks Project in Jiangsu Province(JY-059)the 333 Project in Jiangsu Province and the Fundamental Research Funds for the Central Universities of CUMT(2024ZDPYJQ1003).
文摘In this work,we study wave state transitions of the(2+1)-dimensional Kortewegde Vries-Sawada-Kotera-Ramani(2KdVSKR)equation by analyzing the characteristic line and phase shift.By converting the wave parameters of the N-soliton solution into complex numbers,the breath wave solution is constructed.The lump wave solution is derived through the long wave limit method.Then,by choosing appropriate parameter values,we acquire a number of transformed nonlinear waves whose gradient relation is discussed according to the ratio of the wave parameters.Furthermore,we reveal transition mechanisms of the waves by exploring the nonlinear superposition of the solitary and periodic wave components.Subsequently,locality,oscillation properties and evolutionary phenomenon of the transformed waves are presented.And we also prove the change in the geometrical properties of the characteristic lines leads to the phenomena of wave evolution.Finally,for higher-order waves,a range of interaction models are depicted along with their evolutionary phenomena.And we demonstrate that their diversity is due to the fact that the solitary and periodic wave components produce different phase shifts caused by time evolution and collisions.
基金financially supported by the Scientific Research Foundation of North China University of Technology (Grant Nos.11005136024XN147-87 and 110051360024XN151-86)。
文摘Recently, during the investigations on planetary oceans, Hirota-Satsuma-Ito-type models have been developed. In this paper, for a(2+1)-dimensional generalized variable-coefficient Hirota-Satsuma-Ito system describing the fluid dynamics of shallow-water waves in an open ocean, non-characteristic movable singular manifold and symbolic computation enable an oceanic auto-B?cklund transformation with three sets of the oceanic solitonic solutions. The results rely on the oceanic variable coefficients in that system. Future oceanic observations might detect some nonlinear features predicted in this paper, and relevant oceanographic insights might be expected.
基金This work was funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘Most existing 2-dimensional barcodes are designed with a fixed shape and clear area.Having a fixed shape and clear area makes the barcode difficult to lay out with other text and pictures.To solve this problem,an amorphous 2-dimensional barcode is presented in this paper.The barcode uses encoding graph units to encode data.There are two key points in a 2-dimensional barcode:One is the encoding graph unit,the other is its encoding rules.Because encoding graph units of a 2-dimensional barcode are surrounded by other graphics,the units should be self-positioned and distinguished from other units.This paper presents an encoding graph unit generation algorithm,which is based on genetic algorithms.Encoding rules of the barcode are also given in this paper.Those rules include data encoding rules and encoding graph unit sequence arrangement rules.Data encoding rules are used to encode data to an encoding graph unit sequence.Encoding graph unit sequence arrangement rules are used to embed the unit sequence in the target picture.In addition to those rules,it also discussed the steps to restore encoding graph unit sequence from a picture.In the experiments section of this paper,an example is provided to encode a string and embed it in a car ad picture by the barcode.According to encoding rules of the barcode,those encoding graphic units can be scattered and embedded in a picture with other graphics,so amorphous 2-dimensional barcode has no fixed shape.Take advantage of this,designer can present a more elegant design to lay out barcodes with other graphic elements.
文摘We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.
基金The project supported by National Natural Science Foundation of China
文摘The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.
基金supported by a grant from the Shanghai Municipal Health Bureau(No.054041)
文摘BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and severe PPH, any dramatic hemodynamic changes in liver transplantation or other procedures may result in death from pulmonary and cardiac events. In this study, we investigated the prevalence of PPH in patients with portal hypertension (PHT) mainly caused by hepatitis B virus, and evaluated the effect of 2-dimensional Doppler echocardiography (2D-ECHO) in screening for PPH. METHODS: One hundred and five PHT patients received transthoracic 2D-ECHO preoperatively, systolic pulmonary arterial pressure (SPAP, normal range <30 mmHg) and pulmonary acceleration time (PAT, normal range >= 120 msec) were measured to screen for PPH (positive result: SPAP >= 30 mmHg and/or PAT <100 msec). Subsequently, pulmonary hemodynamic parameters were measured by right heart catheterization (RHC) for definitive diagnosis of PPH. The results of the two methods were compared to assess the screening effect of 2D-ECHO. RESULTS: The prevalence of PPH in this study was 3.8% (4/105). About 90% (95/105) of patients had a detectable tricuspid regurgitation by 2D-ECHO and the mean SPAP was 27.7 +/- 5.9 mmHg. Twenty-two of these 95 patients had an SPAP >30 mmHg. The mean PAT of all patients was 140 23 msec and 5 were <100 msec. Twenty-two patients were screened out by 2D-ECHO and 4 were diagnosed by RHC. A positive significant correlation (r=0.55, P<0.01) was found between SPAP measured by 2D-ECHO and mean pulmonary artery pressure (MPAP) measured by RHC, and a weak but significant negative correlation (r=-0.27, P=0.005) existed between PAT and pulmonary vascular resistance (PVR). The sensitivity, specificity, agreement rate, positive predictive value and negative predictive value of the screening test were 100%, 82%, 83%, 18% and 100%, respectively. CONCLUSIONS: The prevalence of PPH in this study is lower than in Western countries. As a screening test, 2D-ECHO has very high sensitivity and negative predictive value. A negative test result can directly be used to exclude PPH, while a positive result should be confirmed by RHC.
基金The project supported by the Natural Science Foundation of Shandong Province of China under Grant No. 2004 zx 16
文摘Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.
基金Supported by the Global Change Research Program of China under Grant No.2015CB953904National Natural Science Foundation of China under Grant Nos.11675054 and 11435005+1 种基金Outstanding Doctoral Dissertation Cultivation Plan of Action under Grant No.YB2016039Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things under Grant No.ZF1213
文摘In this paper, a class of lump solutions to the (2+1)-dimensional Sawada–Kotera equation is studied by searching for positive quadratic function solutions to the associated bilinear equation. To guarantee rational localization and analyticity of the lumps, some sufficient and necessary conditions are presented on the parameters involved in the solutions. Then, a completely non-elastic interaction between a lump and a stripe of the(2+1)-dimensional Sawada–Kotera equation is obtained, which shows a lump solution is drowned or swallowed by a stripe soliton. Finally, 2-dimensional curves, 3-dimensional plots and density plots with particular choices of the involved parameters are presented to show the dynamic characteristics of the obtained lump and interaction solutions.
基金The project supported by National Natural Science Foundation of China, the Natural Science Foundation of Shandong Province of China, and the Natural Science Foundation of Liaocheng University .
文摘In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.
文摘A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.
文摘New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000 .
文摘In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11175092,11275123,11205092,and 10905038Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213+1 种基金Talent FundK.C.Wong Magna Fund in Ningbo University
文摘The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11075055,11275072Innovative Research Team Program of the National Science Foundation of China under Grant No.61021104+3 种基金National High Technology Research and Development Program under Grant No.2011AA010101Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213Talent FundK.C.Wong Magna Fund in Ningbo University
文摘Two Darboux transformations of the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawaka(CDGKS)equation and(2+1)-dimensional modified Korteweg-de Vries(mKdV) equation are constructed through the Darboux matrix method, respectively. N-soliton solutions of these two equations are presented by applying the Darboux transformations N times. The right-going bright single-soliton solution and interactions of two and three-soliton overtaking collisions of the(2+1)-dimensional CDGKS equation are studied. By choosing different seed solutions, the right-going bright and left-going dark single-soliton solutions, the interactions of two and three-soliton overtaking collisions, and kink soliton solutions of the(2+1)-dimensional mKdV equation are investigated. The results can be used to illustrate the interactions of water waves in shallow water.
基金supported by National Natural Science Foundation of China under Grant Nos.11775121 and 11435005K C Wong Magna Fund in Ningbo University。
文摘In this paper,based on N-soliton solutions,we introduce a new constraint among parameters to find the resonance Y-type soliton solutions in(2+1)-dimensional integrable systems.Then,we take the(2+1)-dimensional Sawada–Kotera equation as an example to illustrate how to generate these resonance Y-type soliton solutions with this new constraint.Next,by the long wave limit method,velocity resonance and module resonance,we can obtain some new types of hybrid solutions of resonance Y-type solitons with line waves,breather waves,high-order lump waves respectively.Finally,we also study the dynamics of these interaction solutions and indicate mathematically that these interactions are elastic.
基金Supported by the National Natural Science Foundation of China under Grant No.11275072Research Fund for the Doctoral Program of Higher Education of China under Grant No.20120076110024+3 种基金Innovative Research Team Program of the National Natural Science Foundation of China under Grant No.61321064Shanghai Knowledge Service Platform Project under Grant No.ZF1213Shanghai Minhang District Talents of High Level Scientific Research ProjectTalent Fund and K.C.Wong Magna Fund in Ningbo University
文摘In this paper, a detailed Lie symmetry analysis of the(2+1)-dimensional coupled nonlinear extension of the reaction-diffusion equation is presented. The general finite transformation group is derived via a simple direct method,which is equivalent to Lie point symmetry group actually. Similarity reduction and some exact solutions of the original equation are obtained based on the optimal system of one-dimensional subalgebras. In addition, conservation laws are constructed by employing the new conservation theorem.
文摘Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.
基金Project supported by the Natural Science Foundation of Guangdong Province of China (Grant No.10452840301004616)the National Natural Science Foundation of China (Grant No.61001018)the Scientific Research Foundation for the Doctors of University of Electronic Science and Technology of China Zhongshan Institute (Grant No.408YKQ09)
文摘Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.
基金Supported by the National Natural Science Foundation of China under Grant Nos.10771196 and 10831003the Natural Science Foundation of Zhejiang Province under Grant Nos.Y7080198 and R6090109
文摘In this paper, the （2＋ 1）-dimensional soliton equation is mainly being discussed. Based on the Hirota direct method, Wronskian technique and the Pfattlan properties, the N-soliton solution, Wronskian and Grammian solutions have been generated.
