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Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation
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作者 巩乾坤 王惠 王云虎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期409-416,共8页
This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional ... This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs. 展开更多
关键词 lump solution rogue wave solution breather wave solution (2+1)-dimensional Hirota-Satsuma-Ito equation
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Dynamics of Nonlinear Waves in(2+1)-Dimensional Extended Boiti-Leon-Manna-Pempinelli Equation
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作者 SUN Junxiu WANG Yunhu 《应用数学》 北大核心 2024年第4期1103-1113,共11页
Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamic... Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton. 展开更多
关键词 Hirota bilinear method N-soliton solutions Breather solutions Lump solutions Interaction solutions (2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation
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Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation
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作者 Dahe Feng Jibin Li Airen Zhou 《Applied Mathematics》 2024年第8期543-567,共25页
For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits ... For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation. 展开更多
关键词 (2 + 1)-dimensional Nonlinear Dispersive Boussinesq equation BIFURCATIONS Phase Portrait Analytical Periodic Wave Solution Periodic Cusp Wave Solution
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New Complexiton Solutions of (2+1)-Dimensional Nizhnik-Novikov-Veselov Equations 被引量:5
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作者 ZHANG Yuan-Yuan ZHENG Ying ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第3X期407-414,共8页
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
关键词 rational expansion method (2+1)-dimensional nizhnik-Novikov-Veselov equations complexiton solutions
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MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A(2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION 被引量:1
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作者 李岩 姚若侠 夏亚荣 《Acta Mathematica Scientia》 SCIE CSCD 2023年第1期80-96,共17页
Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmet... Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic. 展开更多
关键词 (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt equation soliton molecules velocity resonance nonelastic interaction
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Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation
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作者 庞福忠 葛根哈斯 赵雪梅 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第5期200-217,共18页
The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions ... The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations. 展开更多
关键词 (2+1)-dimensional elliptic Toda equation resonant interaction lump molecules
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Interaction solutions and localized waves to the(2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient
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作者 闫鑫颖 刘锦洲 辛祥鹏 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第7期199-205,共7页
This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé... This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature. 展开更多
关键词 (2+1)-dimensional variable coefficient Hirota-Satsuma-Ito equation Hirota bilinear method long wave limit method N-soliton solutions
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New exact periodic solutions to (2+1)-dimensional dispersive long wave equations 被引量:2
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作者 张文亮 吴国将 +2 位作者 张苗 王军帽 韩家骅 《Chinese Physics B》 SCIE EI CAS CSCD 2008年第4期1156-1164,共9页
In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are... In this paper, we make use of the auxiliary equation and the expanded mapping methods to find the new exact periodic solutions for (2+1)-dimensional dispersive long wave equations in mathematical physics, which are expressed by Jacobi elliptic functions, and obtain some new solitary wave solutions (m → 1). This method can also be used to explore new periodic wave solutions for other nonlinear evolution equations. 展开更多
关键词 auxiliary equation method expanded mapping method (2+1)-dimensional dispersivelong wave equations periodic wave solutions
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A New Class of Periodic Solutions to (2+1)-Dimensional KdV Equations 被引量:1
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作者 HUANG Wen-Hua LIU Yu-Lu +1 位作者 ZHANG Jie-Fang LAI Xian-Jing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第3X期401-406,共6页
We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations... We investigate a new class of periodic solutions to (2+1)-dimensional KdV equations, by both the linear superposition approach and the mapping deformation method. These new periodic solutions are suitable combinations of the periodic solutions to the (2+1)-dimensional KdV equations obtained by means of the Jacobian elliptic function method, but they possess different periods and velocities. 展开更多
关键词 (2+1)-dimensional KdV equation linear superposition periodic solution
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On an Auto-Baecklund Transformation for (2+1)-Dimensional VariableCoefficient Generalized KP Equations and Exact Solutions 被引量:1
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作者 BAICheng-Jie BAICheng-Lin +1 位作者 HANJi-Guang ZHAOHong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第4期677-680,共4页
By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two ... By the application of the extended homogeneous balance method, we derive anauto-Backlund transformation (BT) for (2+1)-dimensional variable coefficient generalized KPequations. Based on the BT, in which there are two homogeneity equations to be solved, we obtainsome exact solutions containing single solitary waves. 展开更多
关键词 extended homogeneous balance method (2+1)-dimensional variable coefficientgeneralized KP equation auto-Baecklund transformation exact solutions
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LOCALIZED COHERENT STRUCTURES OF THE (2+1)-DIMENSIONAL HIGHER ORDER BROER-KAUP EQUATIONS
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作者 ZHANG Jie-fang(张解放) +1 位作者 LIU Yu-lu(刘宇陆) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第5期549-556,共8页
By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended hom... By using the extended homogeneous balance method, the localized coherent structures are studied. A nonlinear transformation was first established, and then the linearization form was obtained based on the extended homogeneous balance method for the higher order (2 + 1)-dimensional Broer-Kaup equations. Starting from this linearization form equation, a variable separation solution with the entrance of some arbitrary functions and some arbitrary parameters was constructed. The quite rich localized coherent structures were revealed. This method, which can be generalized to other (2 + I) -dimensional nonlinear evolution equation, is simple and powerful. 展开更多
关键词 higher order Broer-Kaup equation (2+1)-dimension coherent structure homogeneous balance method
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New Families of Rational Form Variable Separation Solutions to(2+1)-Dimensional Dispersive Long Wave Equations
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作者 WEN Xiao-Yong 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第5期789-793,共5页
With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transfor... With the aid of symbolic computation system Maple, some families of new rational variable separation solutions of the (2+1)-dimensional dispersive long wave equations are constructed by means of a function transformation, improved mapping approach, and variable separation approach, among which there are rational solitary wave solutions, periodic wave solutions and rational wave solutions. 展开更多
关键词 improved mapping approach variable separation method (2+1)-dimensional dispersive long wave equations symbolic computation
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Painlevé Analysis,Soliton Solutions and Bcklund Transformation for Extended (2 + 1)-Dimensional Konopelchenko-Dubrovsky Equations in Fluid Mechanics via Symbolic Computation
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作者 许鹏博 高以天 +2 位作者 于鑫 王雷 林国栋 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第6期1017-1023,共7页
This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plas... This paper is to investigate the extended(2+1)-dimensional Konopelchenko-Dubrovsky equations,which can be applied to describing certain phenomena in the stratified shear flow,the internal and shallow-water waves, plasmas and other fields.Painleve analysis is passed through via symbolic computation.Bilinear-form equations are constructed and soliton solutions are derived.Soliton solutions and interactions are illustrated.Bilinear-form Backlund transformation and a type of solutions are obtained. 展开更多
关键词 extended (2 1-dimensional Konopelchenko-Dubrovsky equations in fluid mechanics Painleve analysis soliton solutions Backlund transformation symbolic computation
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Study on (2+1)-Dimensional Nizhnik-Novikov-Veselov Equation by Using Extended Mapping Approach
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作者 XU Chang-Zhi HE Bao-Gang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第1X期10-14,共5页
Extended mapping approach is introduced to solve (2+1)-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excit... Extended mapping approach is introduced to solve (2+1)-dimensional Nizhnik-Novikov Veselov equation. A new type of variable separation solutions is derived with arbitrary functions in the model. Based on this excitation, rich localized structures such as multi-lump soliton and ring soliton are revealed by selecting the arbitrary function appropriately. 展开更多
关键词 extended mapping approach (2+1)-dimensional nizhnik-Novikov-Veselov equation new localized excitation
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Symmetry Groups and New Exact Solutions of(2+1)-Dimensional Dispersive Long-Wave Equations
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作者 TIAN Ying-Hui CHEN Han-Lin LIU Xi-Qiang 《Communications in Theoretical Physics》 SCIE CAS CSCD 2009年第5期781-784,共4页
Using the modified CK's direct method, we derive a symmetry group theorem of (2+1)-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of (2+1)-... Using the modified CK's direct method, we derive a symmetry group theorem of (2+1)-dimensional dispersive long-wave equations. Based upon the theorem, Lie point symmetry groups and new exact solutions of (2+1)- dimensional dispersive long-wave equations are obtained. 展开更多
关键词 (2+1)-dimensional dispersive long-wave equations exact solution modified CK's direct method symmetry groups
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Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation 被引量:8
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作者 ZHANG Jie-Fang HUANG Wen-Hua ZHENG Chun-Long 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第11期517-522,共6页
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
关键词 variable separation approach coherent structures NEW (2+1)-dimensional SOLITON equation
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New Exact Solutions for (2+1)-Dimensional Breaking Soliton Equation 被引量:6
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作者 PENGYan-Ze 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第2期205-207,共3页
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
关键词 exact solutions (2+1)-dimensional breaking soliton equation modifiedmapping method
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Symmetry Groups and New Exact Solutions to (2+1)-Dimensional Variable Coefficient Canonical Generalized KP Equation 被引量:7
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作者 ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第3X期405-410,共6页
In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation... In this paper, the modified CK's direct method to find symmetry groups of nonlinear partial differential equation is extended to (2+1)-dimensional variable coeffficient canonical generalized KP (VCCGKP) equation. As a result, symmetry groups, Lie point symmetry group and Lie symmetry for the VCCGKP equation are obtained. In fact, the Lie point symmetry group coincides with that obtained by the standard Lie group approach. Applying the given Lie symmetry, we obtain five types of similarity reductions and a lot of new exact solutions, including hyperbolic function solutions, triangular periodic solutions, Jacobi elliptic function solutions and rational solutions, for the VCCGKP equation. 展开更多
关键词 (2+1)-dimensional variable coefficient canonical generalized KP (VCCGKP) equation modified CK's'direct method symmetry groups Lie symmetry similarity reductions new exact solutions
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Wronskian and Grammian Solutions for(2+1)-Dimensional Soliton Equation 被引量:3
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作者 张翼 程腾飞 +1 位作者 丁大军 党小兰 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第1期20-24,共5页
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
关键词 Hirota bilinear method Wronskian solution Grammian solution (2+1)-dimensional soliton equation
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The Travelling Wave Solutions for (2+1)-dimensional AKNS Equation 被引量:3
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作者 程智龙 郝晓红 《Chinese Quarterly Journal of Mathematics》 2015年第3期323-329,共7页
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
关键词 (2+1)-dimensional AKNS equatION SOLITON SOLUTION
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