This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The m...This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The motion of the fluid is taken as two-dimensional with the impact of a magnetic field in the normal direction. The variable, permeable, and stretching nature of sheet's surface sets the fluid into motion. Thermal and mass diffusions are controlled through the use of the Cattaneo–Christov flux model. A dataset is generated using MATLAB bvp4c package solver and employed to train an artificial neural network(ANN) based on the Levenberg–Marquardt back-propagation(LMBP) algorithm. It has been observed as an outcome of this study that the modeled problem achieves peak performance at epochs 637, 112, 4848, and 344 using ANN-LMBP. The linear velocity of the fluid weakens with progression in variable porous and magnetic factors.With an augmentation in magnetic factor, the micro-rotational velocity profiles are augmented on the domain 0 ≤ η < 1.5 due to the support of micro-rotations by Lorentz forces close to the sheet's surface, while they are suppressed on the domain 1.5 ≤ η < 6.0 due to opposing micro-rotations away from the sheet's surface. Thermal distributions are augmented with an upsurge in thermophoresis, Brownian motion, magnetic, and radiation factors, while they are suppressed with an upsurge in thermal relaxation parameter. Concentration profiles increase with an expansion in thermophoresis factor and are suppressed with an intensification of Brownian motion factor and solute relaxation factor. The absolute errors(AEs) are evaluated for all the four scenarios that fall within the range 10^(-3)–10^(-8) and are associated with the corresponding ANN configuration that demonstrates a fine degree of accuracy.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
Security assessment can help understand the security conditions of an information system and yield results highly conducive to the solution of security problems in it. Taking the computer networks in a certain univers...Security assessment can help understand the security conditions of an information system and yield results highly conducive to the solution of security problems in it. Taking the computer networks in a certain university as samples, this paper, with the information system security assessment model as its foundation, proposes a multi-attribute group decision-making （MAGDM） security assessment method based on a variable consistency dominance-based rough set approach （VC-DRSA）. This assessment method combines VC-DRSA with the analytic hierarchy process （AHP）, uncovers the inherent information hidden in data via the quality of sorting （QoS）, and makes a synthetic security assessment of the information system after determining the security attribute weight. The sample findings show that this method can effectively remove the bottleneck of MAGDM, thus assuming practical significance in information system security assessment.展开更多
After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations b...After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schr?dinger equation as a concrete example, the method is recommended in detail.展开更多
By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal...By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.展开更多
The second-order backward differential formula(BDF2)and the scalar auxiliary variable(SAV)approach are applied to con‐struct the linearly energy stable numerical scheme with the variable time steps for the epitaxial ...The second-order backward differential formula(BDF2)and the scalar auxiliary variable(SAV)approach are applied to con‐struct the linearly energy stable numerical scheme with the variable time steps for the epitaxial thin film growth models.Under the stepratio condition 0<τ_(n)/τ_(n-1)<4.864,the modified energy dissipation law is proven at the discrete levels with regardless of time step size.Nu‐merical experiments are presented to demonstrate the accuracy and efficiency of the proposed numerical scheme.展开更多
By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized co...By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations — compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.展开更多
In this letter, starting from a B?cklund transformation, a general solution of a (2+1)-dimensional integrable system is obtained by using the new variable separation approach.
The multi-linear variable separation approach (MLVSA ) is very useful to solve (2+ 1)-dimensional integrable systems. In this letter, we extend this method to solve a (1+1)-dimensional coupled integrable dispersion-le...The multi-linear variable separation approach (MLVSA ) is very useful to solve (2+ 1)-dimensional integrable systems. In this letter, we extend this method to solve a (1+1)-dimensional coupled integrable dispersion-less system.Namely, by using a Backlund transformation and the MLVSA, we find a new general solution and define a new "universal formula". Then, some new (1+1)-dimensional coherent structures of this universal formula can be found by selecting corresponding functions appropriately. Specially, in some conditions, bell soliton and kink soliton can transform each other, which are illustrated graphically.展开更多
The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burge...The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burgers system, (2+1)-dimensional breaking soliton system, and (2+1)-dimensional Maccari system. Some new exact solutions are obtained and the universal formula obtained from many (2+1)-dimensional systems is extended or modified.展开更多
With the application of 2.5D Woven Variable Thickness Composites(2.5DWVTC)in aviation and other fields,the issue of strength failure in this composite type has become a focal point.First,a three-step modeling approach...With the application of 2.5D Woven Variable Thickness Composites(2.5DWVTC)in aviation and other fields,the issue of strength failure in this composite type has become a focal point.First,a three-step modeling approach is proposed to rapidly construct full-scale meso-finite element models for Outer Reduction Yarn Woven Composites(ORYWC)and Inner Reduction Yarn Woven Composites(IRYWC).Then,six independent damage variables are identified:yarn fiber tension/compression,yarn matrix tension/compression,and resin matrix tension/compression.These variables are utilized to establish the constitutive equation of woven composites,considering the coupling effects of microscopic damage.Finally,combined with the Hashin failure criterion and von Mises failure criterion,the strength prediction model is implemented in ANSYS using APDL language to simulate the strength failure process of 2.5DWVTC.The results show that the predicted stiffness and strength values of various parts of ORYWC and IRYWC are in good agreement with the relevant test results.展开更多
A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, u...A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.展开更多
The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the GreenLindsay(G-L) theory, the coupled(CD) theory, and the Lord-Shulman(...The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the GreenLindsay(G-L) theory, the coupled(CD) theory, and the Lord-Shulman(L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock.The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.展开更多
Reasonable and effective fatigue load spectrum is key of aircraft structural fatigue test.Two kinds of load spectra simplification approaches based on statistical consistent fatigue damage model are proposed in the pa...Reasonable and effective fatigue load spectrum is key of aircraft structural fatigue test.Two kinds of load spectra simplification approaches based on statistical consistent fatigue damage model are proposed in the paper.One method is to simplify the original multi-level load spectra to spectral load with fewer level and was verified by the experimental data of five levels and seven levels load spectra.The equivalent damage here is not equivalent fatigue life,but equivalent number of spectral blocks.Moreover,it was proved that a section of low stress load cannot be converted into the highest stress load considering equivalent damage.The other is to convert the life distribution under multi-level load spectra into that of constant amplitude spectrum according to a certain principle,that is,equivalent damage is achieved through equivalent fatigue life,and two groups of three levels spectral data were used for experimental verification.The results show that equivalent damage simplification approach of multi-level load spectra is feasible,and it achieve that the damage of one loading block before and after the simplification is equal in probability statistics.The life distribution of load simplified as constant amplitude spectrum is consistent with test data.The simplification method presented in this paper can be generalized and is a predictive engineering method which does not depend on experimental data.展开更多
A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variati...A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variational equations which give the evolution of the light pulses parameters as a function of the propagation distance. The collective coordinate approach is incomparably faster than the direct numerical simulation of the propagation equation. This allows us to obtain, efficiently, a global mapping of the 3D pulsating soliton. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics.展开更多
Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers syst...Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.展开更多
A variable separation approach is proposed and extended to the （1＋1）-dimensional physics system. The variable separation solution of （1-F1）-dimensional Ito system is obtained. Some special types of solutions such...A variable separation approach is proposed and extended to the （1＋1）-dimensional physics system. The variable separation solution of （1-F1）-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.展开更多
Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solu...Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solutions, periodic-soliton solutions, and Weierstrass function solutions. Based on a periodic-soliton solution, a new type of localized excitation, i.e., the four-dromion soliton, is constructed and some evolutional properties of this localized structure are briefly discussed.展开更多
We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, givi...We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, giving the evolution of the light pulses parameters as a function of the propagation distance. The collective variables approach permits us to obtain, efficiently, a global mapping of the 3D stationary dissipative solitons. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics. Thus it helps to show the impact of dispersion and nonlinear gain on the stationary dynamic.展开更多
Variable separation approach is introduced to solve the （2＋1）-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation m...Variable separation approach is introduced to solve the （2＋1）-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model （24）. Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.展开更多
基金the Deanship of Research and Graduate Studies at King Khalid University for funding this work through large Research Group Project (Grant No. RGP2/198/45)Project supported by Prince Sattam bin Abdulaziz University (Grant No. PSAU/2025/R/1446)。
文摘This work investigates water-based micropolar hybrid nanofluid(MHNF) flow on an elongating variable porous sheet.Nanoparticles of diamond and copper have been used in the water to boost its thermal conductivity. The motion of the fluid is taken as two-dimensional with the impact of a magnetic field in the normal direction. The variable, permeable, and stretching nature of sheet's surface sets the fluid into motion. Thermal and mass diffusions are controlled through the use of the Cattaneo–Christov flux model. A dataset is generated using MATLAB bvp4c package solver and employed to train an artificial neural network(ANN) based on the Levenberg–Marquardt back-propagation(LMBP) algorithm. It has been observed as an outcome of this study that the modeled problem achieves peak performance at epochs 637, 112, 4848, and 344 using ANN-LMBP. The linear velocity of the fluid weakens with progression in variable porous and magnetic factors.With an augmentation in magnetic factor, the micro-rotational velocity profiles are augmented on the domain 0 ≤ η < 1.5 due to the support of micro-rotations by Lorentz forces close to the sheet's surface, while they are suppressed on the domain 1.5 ≤ η < 6.0 due to opposing micro-rotations away from the sheet's surface. Thermal distributions are augmented with an upsurge in thermophoresis, Brownian motion, magnetic, and radiation factors, while they are suppressed with an upsurge in thermal relaxation parameter. Concentration profiles increase with an expansion in thermophoresis factor and are suppressed with an intensification of Brownian motion factor and solute relaxation factor. The absolute errors(AEs) are evaluated for all the four scenarios that fall within the range 10^(-3)–10^(-8) and are associated with the corresponding ANN configuration that demonstrates a fine degree of accuracy.
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Supported by the High Technology Research and Development Programme of China (No. 2007AA01Z473)
文摘Security assessment can help understand the security conditions of an information system and yield results highly conducive to the solution of security problems in it. Taking the computer networks in a certain university as samples, this paper, with the information system security assessment model as its foundation, proposes a multi-attribute group decision-making （MAGDM） security assessment method based on a variable consistency dominance-based rough set approach （VC-DRSA）. This assessment method combines VC-DRSA with the analytic hierarchy process （AHP）, uncovers the inherent information hidden in data via the quality of sorting （QoS）, and makes a synthetic security assessment of the information system after determining the security attribute weight. The sample findings show that this method can effectively remove the bottleneck of MAGDM, thus assuming practical significance in information system security assessment.
基金国家自然科学基金，浙江省自然科学基金，Foundation of State Key Laboratory of Oil/Gas Reservoir Geology and Exploitation (PLN 0104)，the Foundation of Educational Commission，浙江省宁波市博士基金
文摘After considering the variable coefficient of a nonlinear equation as a new dependent variable, some special types of variable-coefficient equation can be solved from the corresponding constant-coefficient equations by using the general classical Lie approach. Taking the nonlinear Schr?dinger equation as a concrete example, the method is recommended in detail.
文摘By using a Baecklund transformation and the multi-linear variable separationapproach, we find a new general solution of a (2+1)-dimensional generalization of the nonlinearSchroedinger system. The new 'universal' formula is defined, and then, rich coherent structures canbe found by selecting corresponding functions appropriately.
文摘The second-order backward differential formula(BDF2)and the scalar auxiliary variable(SAV)approach are applied to con‐struct the linearly energy stable numerical scheme with the variable time steps for the epitaxial thin film growth models.Under the stepratio condition 0<τ_(n)/τ_(n-1)<4.864,the modified energy dissipation law is proven at the discrete levels with regardless of time step size.Nu‐merical experiments are presented to demonstrate the accuracy and efficiency of the proposed numerical scheme.
基金The project supported by National Natural Science Foundation of China under Grant No.10172056+2 种基金the Natural Science Foundation of Zhengjiang Provincethe Foundation of Zhengjiang Lishui College under Grant Nos.KZ03009 and KZ03005
文摘By means of the standard truncated Painlevé expansion and a variable separation approach, a general variable separation solution of the generalized Burgers system is derived. In addition to the usual localized coherent soliton excitations like dromions, lumps, rings, breathers, instantons, oscillating soliton excitations, peakons, foldons, and previously revealed chaotic and fractal localized solutions, some new types of excitations — compacton and Jacobi periodic wave solutions are obtained by introducing appropriate lower dimensional piecewise smooth functions and Jacobi elliptic functions.
文摘In this letter, starting from a B?cklund transformation, a general solution of a (2+1)-dimensional integrable system is obtained by using the new variable separation approach.
文摘The multi-linear variable separation approach (MLVSA ) is very useful to solve (2+ 1)-dimensional integrable systems. In this letter, we extend this method to solve a (1+1)-dimensional coupled integrable dispersion-less system.Namely, by using a Backlund transformation and the MLVSA, we find a new general solution and define a new "universal formula". Then, some new (1+1)-dimensional coherent structures of this universal formula can be found by selecting corresponding functions appropriately. Specially, in some conditions, bell soliton and kink soliton can transform each other, which are illustrated graphically.
文摘The multi-linear variable separation approach method is very useful to solve (2+1)-dimensional integrable systems. In this letter, we extend this method to solve (1+1)-dimensional Boiti system, (2+1)-dimensional Burgers system, (2+1)-dimensional breaking soliton system, and (2+1)-dimensional Maccari system. Some new exact solutions are obtained and the universal formula obtained from many (2+1)-dimensional systems is extended or modified.
基金supported by National Science and Technology Major Project,China(No.2017-IV-0007-0044)National Natural Science Foundation of China(No.52175142),National Natural Science Foundation of China(No.52305170)Natural Science Foundation of Sichuan Province,China(No.2022NSFSC1885)。
文摘With the application of 2.5D Woven Variable Thickness Composites(2.5DWVTC)in aviation and other fields,the issue of strength failure in this composite type has become a focal point.First,a three-step modeling approach is proposed to rapidly construct full-scale meso-finite element models for Outer Reduction Yarn Woven Composites(ORYWC)and Inner Reduction Yarn Woven Composites(IRYWC).Then,six independent damage variables are identified:yarn fiber tension/compression,yarn matrix tension/compression,and resin matrix tension/compression.These variables are utilized to establish the constitutive equation of woven composites,considering the coupling effects of microscopic damage.Finally,combined with the Hashin failure criterion and von Mises failure criterion,the strength prediction model is implemented in ANSYS using APDL language to simulate the strength failure process of 2.5DWVTC.The results show that the predicted stiffness and strength values of various parts of ORYWC and IRYWC are in good agreement with the relevant test results.
基金supported by the National Natural Science Foundation of China (No.10972084)
文摘A new computation scheme proposed to tackle commensurate problems is devel- oped by modifying the semi-analytic approach for minimizing computational complexity. Using the proposed scheme, the limit state equations, usually referred to as the failure surface, are obtained from transformation of an interval variable to a normalized one. In order to minimize the computational cost, two algorithms for optimizing the calculation steps have been proposed. The monotonicity of the objective function can be determined from narrowing the scope of interval variables in normalized infinite space by incorporating the algorithms into the computational scheme. Two examples are used to illustrate the operation and computational efficiency of the approach. The results of these examples show that the proposed algorithms can greatly reduce the computation complexity without sacrificing the computational accuracy. The advantage of the proposed scheme can be even more efficient for analyzing sophistic structures.
文摘The basic equations for a homogeneous and isotropic thermo-magnetoviscoelastic medium are formulated based on three different theories, i.e., the GreenLindsay(G-L) theory, the coupled(CD) theory, and the Lord-Shulman(L-S) theory. The variable thermal conductivity is considered as a linear function of the temperature. Using suitable non-dimensional variables, these basic equations are solved via the eigenvalue approach. The medium is initially assumed to be stress-free and subject to a thermal shock.The numerical results reveal that the viscosity, the two-temperature parameter, the gravity term, and the magnetic field significantly influence the distribution of the physical quantities of the thermoelastic medium.
文摘Reasonable and effective fatigue load spectrum is key of aircraft structural fatigue test.Two kinds of load spectra simplification approaches based on statistical consistent fatigue damage model are proposed in the paper.One method is to simplify the original multi-level load spectra to spectral load with fewer level and was verified by the experimental data of five levels and seven levels load spectra.The equivalent damage here is not equivalent fatigue life,but equivalent number of spectral blocks.Moreover,it was proved that a section of low stress load cannot be converted into the highest stress load considering equivalent damage.The other is to convert the life distribution under multi-level load spectra into that of constant amplitude spectrum according to a certain principle,that is,equivalent damage is achieved through equivalent fatigue life,and two groups of three levels spectral data were used for experimental verification.The results show that equivalent damage simplification approach of multi-level load spectra is feasible,and it achieve that the damage of one loading block before and after the simplification is equal in probability statistics.The life distribution of load simplified as constant amplitude spectrum is consistent with test data.The simplification method presented in this paper can be generalized and is a predictive engineering method which does not depend on experimental data.
文摘A semi-analytical approach for the pulsating solutions of the 3D complex Cubic-quintic Ginzburg-Landau Equation (CGLE) is presented in this article. A collective variable approach is used to obtain a system of variational equations which give the evolution of the light pulses parameters as a function of the propagation distance. The collective coordinate approach is incomparably faster than the direct numerical simulation of the propagation equation. This allows us to obtain, efficiently, a global mapping of the 3D pulsating soliton. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics.
文摘Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.
文摘A variable separation approach is proposed and extended to the （1＋1）-dimensional physics system. The variable separation solution of （1-F1）-dimensional Ito system is obtained. Some special types of solutions such as non-propagating solitary wave solution, propagating solitary wave solution and looped soliton solution are found by selecting the arbitrary function appropriately.
基金supported by National Natural Science Foundation of China under Grant No.10272071the Natural Science Foundation of Zhejiang Province under Grant No.Y606049
文摘Using the mapping approach via the projective Riccati equations, several types of variable separated solutions of the （2＋1）-dimensional Nizhnik-Novikov-Veselov equation are obtained, including multiple-soliton solutions, periodic-soliton solutions, and Weierstrass function solutions. Based on a periodic-soliton solution, a new type of localized excitation, i.e., the four-dromion soliton, is constructed and some evolutional properties of this localized structure are briefly discussed.
文摘We feature the stationary solutions of the 3D complex cubic-quintic Ginzburg-Landau equation (CGLE). Our approach is based on collective variables approach which helps to obtain a system of variational equations, giving the evolution of the light pulses parameters as a function of the propagation distance. The collective variables approach permits us to obtain, efficiently, a global mapping of the 3D stationary dissipative solitons. In addition it allows describing the influence of the parameters of the equation on the various physical parameters of the pulse and their dynamics. Thus it helps to show the impact of dispersion and nonlinear gain on the stationary dynamic.
基金The author would like to thank Profs. Jie-Fang Zhang and Chun-Long Zheng for helpful discussions.
文摘Variable separation approach is introduced to solve the （2＋1）-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model （24）. Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately.
