With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phen...With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.展开更多
This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton）...This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.展开更多
On the bases of N-soliton solutions of Hirota’s bilinear method,high-order rogue wave solutions can be derived by a direct limit method.In this paper,a(3+1)-dimensional Kadomtsev-Petviashvili equation is taken to ill...On the bases of N-soliton solutions of Hirota’s bilinear method,high-order rogue wave solutions can be derived by a direct limit method.In this paper,a(3+1)-dimensional Kadomtsev-Petviashvili equation is taken to illustrate the process of obtaining rogue waves,that is,based on the long-wave limit method,rogue wave solutions are generated by reconstructing the phase parameters of N-solitons.Besides the fundamental pattern of rogue waves,the triangle or pentagon patterns are also obtained.Moreover,the different patterns of these solutions are determined by newly introduced parameters.In the end,the general form of N-order rogue wave solutions are proposed.展开更多
Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pol...Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.展开更多
The(2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper,which describe optical solitons in birefringent fibers.Utilizing the Hirota bilinear...The(2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper,which describe optical solitons in birefringent fibers.Utilizing the Hirota bilinear method,we systematically construct single-and double-periodic lump solutions.To provide a detailed insight into the dynamic behavior of the nonlinear waves,we explore diverse mixed solutions,including bright-dark,W-shaped,multi-peak,and bright soliton solutions.Building upon single-periodic lump solutions,we analyze the dynamics of lump waves on both plane-wave and periodic backgrounds using the long-wave limit method.Moreover,we obtain the interaction solutions involving lumps,periodic lumps,and solitons.The interactions among two solitons,multiple lumps,and mixed waves are illustrated and analyzed.Comparative analysis reveals that these multi-lump solutions exhibit richer dynamical properties than conventional single-lump ones.These results contribute to a deeper understanding of nonlinear systems and may facilitate solving nonlinear problems in nature.展开更多
We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear...We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.展开更多
The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations ...The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.展开更多
The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a c...The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method.From an integrable nonisospectral Ablowitz–Kaup–Newell–Segur equation,we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation.These solutions,including soliton solutions,Jordan-block solutions and interaction solutions,exhibit localized structure,whose dynamics are analyzed with graphical illustration.The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.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
Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform s...Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.展开更多
2N line-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper o...2N line-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper obtains N periodic-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation from the 2N line-soliton solutions.展开更多
2N line-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation can be presented by resorting tothe Hirota bilinear method.In this paper,N periodic-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation...2N line-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation can be presented by resorting tothe Hirota bilinear method.In this paper,N periodic-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equationare obtained from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs.展开更多
In this work,we study a new(2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of parameters.We derive multiple soliton solutions,traveling wave solutions,and...In this work,we study a new(2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of parameters.We derive multiple soliton solutions,traveling wave solutions,and periodic solutions as well.We use the simplified Hirotas method and a variety of ansatze to achieve our goal.展开更多
Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutio...Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.展开更多
We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to th...We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to the extended equations including lump solutions,lump–kink solutions,and two other types of interaction solutions,by solving the underdetermined nonlinear system of algebraic equations for associated parameters.Finally,analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed.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
The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,...The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.展开更多
A coupled(2+1)-dimensional variable coefficient Ginzburg-Landau equation is studied.By virtue of the modified Hirota bilinear method,the bright one-soliton solution of the equation is derived.Some phenomena of soliton...A coupled(2+1)-dimensional variable coefficient Ginzburg-Landau equation is studied.By virtue of the modified Hirota bilinear method,the bright one-soliton solution of the equation is derived.Some phenomena of soliton propagation are analyzed by setting different dispersion terms.The influences of the corresponding parameters on the solitons are also discussed.The results can enrich the soliton theory,and may be helpful in the manufacture of optical devices.展开更多
In the paper, the rational breather soliton and kink solitary wave solution of the (2+1)-dimensional PBLMP equation are obtained by adopting Hirota bilinear method and selecting different test functions. Furthermore, ...In the paper, the rational breather soliton and kink solitary wave solution of the (2+1)-dimensional PBLMP equation are obtained by adopting Hirota bilinear method and selecting different test functions. Furthermore, it has been found that the fusion and degeneration of the kink solitary wave occur when interaction between the rational breather soliton and the kink solitary wave happens. These phenomena are very helpful in researching soliton dynamical complexity in the higher dimensional systems.展开更多
A new(2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov(eANNV)equation is proposed by introducing the additional bilinear terms to the usual ANNV equation.Based on the independent transformatio...A new(2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov(eANNV)equation is proposed by introducing the additional bilinear terms to the usual ANNV equation.Based on the independent transformation,the bilinear form of the eANNV equation is constructed.The lump wave is guaranteed by introducing a positive constant term in the quadratic function.Meanwhile,different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions.For the interaction between the lump wave and one-soliton,the energy of the lump wave and one-soliton can transfer to each other at different times.The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term.The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional,contour and density plots.展开更多
文摘With Hirota＇s bilinear direct method, we study the special coupled KdV system to obtain its new soliton solutions. Then we further discuss soliton evolution, corresponding structures, and interesting interactive phenomena in detail with plot. As a result, we find that after the interaction, the solitons make elastic collision and there are no exchanges of their physical quantities including energy, velocity and shape except the phase shift.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10871117 and 10571110)
文摘This paper studies the coupled Burgers equation and the high-order Boussinesq-Burgers equation. The Hirota bilinear method is applied to show that the two equations are completely integrable. Multiple-kink （soliton） solutions and multiple-singular-kink （soliton） solutions are derived for the two equations.
基金supported by the National Natural Science Foundation of China under Grant Nos.12175111,12235007 and 11975131K.C.Wong Magna Fund in Ningbo University
文摘On the bases of N-soliton solutions of Hirota’s bilinear method,high-order rogue wave solutions can be derived by a direct limit method.In this paper,a(3+1)-dimensional Kadomtsev-Petviashvili equation is taken to illustrate the process of obtaining rogue waves,that is,based on the long-wave limit method,rogue wave solutions are generated by reconstructing the phase parameters of N-solitons.Besides the fundamental pattern of rogue waves,the triangle or pentagon patterns are also obtained.Moreover,the different patterns of these solutions are determined by newly introduced parameters.In the end,the general form of N-order rogue wave solutions are proposed.
基金Supported by the National Natural Science Foundation of China (12074295)。
文摘Hirota method is applied to solve the modified nonlinear Schrodinger equation/the derivative nonlinear Schrodinger equation(MNLSE/DNLSE) under nonvanishing boundary conditions(NVBC) and lead to a single and double-pole soliton solution in an explicit form. The general procedures of Hirota method are presented, as well as the limit approach of constructing a soliton-antisoliton pair of equal amplitude with a particular chirp. The evolution figures of these soliton solutions are displayed and analyzed. The influence of the perturbation term and background oscillation strength upon the DPS is also discussed.
基金supported by the Applied Basic Research Program of Shanxi Province,China(Grant Nos.202403021212253 and 202203021221217).
文摘The(2+1)-dimensional generalized coupled nonlinear Schrödinger equations with a four-wave mixing term are studied in this paper,which describe optical solitons in birefringent fibers.Utilizing the Hirota bilinear method,we systematically construct single-and double-periodic lump solutions.To provide a detailed insight into the dynamic behavior of the nonlinear waves,we explore diverse mixed solutions,including bright-dark,W-shaped,multi-peak,and bright soliton solutions.Building upon single-periodic lump solutions,we analyze the dynamics of lump waves on both plane-wave and periodic backgrounds using the long-wave limit method.Moreover,we obtain the interaction solutions involving lumps,periodic lumps,and solitons.The interactions among two solitons,multiple lumps,and mixed waves are illustrated and analyzed.Comparative analysis reveals that these multi-lump solutions exhibit richer dynamical properties than conventional single-lump ones.These results contribute to a deeper understanding of nonlinear systems and may facilitate solving nonlinear problems in nature.
基金supported by the National Natural Science Foundation of China(Grant Nos.12261131495 and 12475008)the Scientific Research and Developed Fund of Zhejiang A&F University(Grant No.2021FR0009)。
文摘We employ the Hirota bilinear method to systematically derive nondegenerate bright one-and two-soliton solutions,along with degenerate bright-dark two-and four-soliton solutions for the reverse-time nonlocal nonlinear Schr¨odinger equation.Beyond the fundamental nondegenerate one-soliton solution,we have identified and characterized nondegenerate breather bound state solitons,with particular emphasis on their evolution dynamics.
基金supported by the National Key R&D Program of China(Grant No.2022YFA1604200)the National Natural Science Foundation of China(Grant No.12261131495)Institute of Systems Science,Beijing Wuzi University(Grant No.BWUISS21).
文摘The coupled nonlocal nonlinear Schrödinger equations with variable coefficients are researched using the nonstandard Hirota bilinear method.The two-soliton and double-hump one-soliton solutions for the equations are first obtained.By assigning different functions to the variable coefficients,we obtain V-shaped,Y-shaped,wave-type,exponential solitons,and so on.Next,we reveal the influence of the real and imaginary parts of the wave numbers on the double-hump structure based on the soliton solutions.Finally,by setting different wave numbers,we can change the distance and transmission direction of the solitons to analyze their dynamic behavior during collisions.This study establishes a theoretical framework for controlling the dynamics of optical fiber in nonlocal nonlinear systems.
基金supported by the National Natural Science Foundation of China(Grant No.12071432)Zhejiang Provincial Natural Science Foundation(Grant No.LZ24A010007)。
文摘The nonisospectral effectλ_t=α(t)λsatisfied by spectral parameterλopens up a new scheme for constructing localized waves to some nonlinear partial differential equations.In this paper,we perform this effect on a complex nonisospectral nonpotential sine-Gordon equation by the bilinearization reduction method.From an integrable nonisospectral Ablowitz–Kaup–Newell–Segur equation,we construct some exact solutions in double Wronskian form to the reduced complex nonisospectral nonpotential sine-Gordon equation.These solutions,including soliton solutions,Jordan-block solutions and interaction solutions,exhibit localized structure,whose dynamics are analyzed with graphical illustration.The research ideas and methods in this paper can be generalized to other negative order nonisospectral integrable systems.
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.
文摘Hirota＇s bilinear direct method is applied to constructing soliton solutions to a special coupled modified Korteweg- de Vries （mKdV） system. Some physical properties such as the spatiotemporal evolution, waveform structure, interactive phenomena of solitons are discussed, especially in the two-soliton case. It is found that different interactive behaviours of solitary waves take place under different parameter conditions of overtaking collision in this system. It is verified that the elastic interaction phenomena exist in this （1＋1）-dimensional integrable coupled model.
基金supported by the National Key Basic Research Project of China (Grant No 2004CB318000)the National Natural Science Foundation of China (Grant No 10771072)+1 种基金the PhD Program Scholarship Fund of ECNU2008 (Grant No 20080052)the Youth Foundation of Inner Mongolia Normal University, China (Grant No QN07035)
文摘2N line-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation can be presented by resorting to the Hirota bilinear method. By extending the real parameters into complex parameters, this paper obtains N periodic-soliton solutions of the （2＋1）-dimensional Kadomtsev-Petviashvili equation from the 2N line-soliton solutions.
基金supported by the State Key Basic Research Program of China under Grant No.2004CB318000National Natural Science Foundation of China under Grant No.10771072
文摘2N line-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation can be presented by resorting tothe Hirota bilinear method.In this paper,N periodic-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equationare obtained from the 2N line-soliton solutions by selecting the parameters into conjugated complex parameters in pairs.
文摘In this work,we study a new(2+1)-dimensional generalized breaking soliton equation which admits the Painleve property for one special set of parameters.We derive multiple soliton solutions,traveling wave solutions,and periodic solutions as well.We use the simplified Hirotas method and a variety of ansatze to achieve our goal.
基金The project supported by National Natural Science Foundation of China under Grant No.10771196the Natural Science Foundation of Zhejiang Province under Grant No.Y605044
文摘Two new exact, rational and periodic wave solutions are derived for the two-dimensional Boussinesq equation. For the first solution it is obtained by performing an appropriate limiting procedure on the soliton solutions obtained by Hirota bilinear method. The second one in terms of Riemann theta function is explicitly presented by virtue of Hirota bilinear method and its asymptotic property is also analyzed in detail. Moreover, it is of interest to note that classical soliton solutions can be reduced from the periodic wave solutions.
基金Project supported by the Fundamental Research Funds for the Central Universities of China(Grant No.2018RC031)the National Natural Science Foundation of China(Grant No.71971015)+1 种基金the Program of the Co-Construction with Beijing Municipal Commission of Education of China(Grant Nos.B19H100010and B18H100040)the Open Fund of IPOC(BUPT)。
文摘We focus on the localized characteristics of lump and interaction solutions to two extended Jimbo–Miwa equations.Based on the Hirota bilinear method and the test function method,we construct the exact solutions to the extended equations including lump solutions,lump–kink solutions,and two other types of interaction solutions,by solving the underdetermined nonlinear system of algebraic equations for associated parameters.Finally,analysis and graphical simulation are presented to show the dynamical characteristics of our solutions and the interaction behaviors are revealed.
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.
基金Supported by the GUCAS President Grant,the National Natural Science Foundation of China under Grant No.10701076
文摘The Korteweg-de Vries equation with a forcing term is established by recent studies as a simple mathematicalmodel of describing the physics of a shallow layer of fluid subject to external forcing.In the present paper,we study theanalytic solutions to the KdV equation with forcing term by using Hirota's direct method.Several exact solutions aregiven as examples,from which one can see that the same type soliton solutions can be excited by different forced term.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11674036 and 11875008)Beijing Youth Top Notch Talent Support Program,China(Grant No.2017000026833ZK08)+1 种基金Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications,Grant No.IPOC2019ZZ01)Fundamental Research Funds for the Central Universities,China(Grant No.500419305).
文摘A coupled(2+1)-dimensional variable coefficient Ginzburg-Landau equation is studied.By virtue of the modified Hirota bilinear method,the bright one-soliton solution of the equation is derived.Some phenomena of soliton propagation are analyzed by setting different dispersion terms.The influences of the corresponding parameters on the solitons are also discussed.The results can enrich the soliton theory,and may be helpful in the manufacture of optical devices.
基金Supported by National Natural Science Foundation of China under Grant No.11361048
文摘In the paper, the rational breather soliton and kink solitary wave solution of the (2+1)-dimensional PBLMP equation are obtained by adopting Hirota bilinear method and selecting different test functions. Furthermore, it has been found that the fusion and degeneration of the kink solitary wave occur when interaction between the rational breather soliton and the kink solitary wave happens. These phenomena are very helpful in researching soliton dynamical complexity in the higher dimensional systems.
基金supported by the National Natural Science Foundation of China Nos.11775146 and 12105243the Natural Science Foundation of Zhejiang Province of China Grant No.LQ22A050002。
文摘A new(2+1)-dimensional higher-order extended asymmetric Nizhnik-Novikov-Veselov(eANNV)equation is proposed by introducing the additional bilinear terms to the usual ANNV equation.Based on the independent transformation,the bilinear form of the eANNV equation is constructed.The lump wave is guaranteed by introducing a positive constant term in the quadratic function.Meanwhile,different class solutions of the eANNV equation are obtained by mixing the quadratic function with the exponential functions.For the interaction between the lump wave and one-soliton,the energy of the lump wave and one-soliton can transfer to each other at different times.The interaction between a lump and two-soliton can be obtained only by eliminating the sixth-order bilinear term.The dynamics of these solutions are illustrated by selecting the specific parameters in three-dimensional,contour and density plots.
