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New Exact Solutions for (2+1)-Dimensional Breaking Soliton Equation 被引量:5
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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 精确解 孤波断裂方程 修正映射法 雅可比偏微分方程 非线性
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Two Classes of New Exact Solutions to (2+1)-Dimensional Breaking Soliton Equation 被引量:2
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作者 PENG Yan-Ze E.V. Krishnan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第5X期807-809,共3页
The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of t... The singular manifold method is used to obtain two general solutions to a (2+1)-dimensional breaking soliton equation, each of which contains two arbitrary functions. Then the new periodic wave solutions in terms of the Jacobi elliptic functions are generated from the general solutions. The long wave limit yields the new types of dromion and solitary structures. 展开更多
关键词 孤波方程 流形结构 周期波 精确解 Painleve扩展
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New Soliton-like Solutions for (2+1)-Dimensional Breaking Soliton Equation
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作者 XIEZheng ZHANGHong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第3期401-406,共6页
The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kind... The (2+1)-dimensional breaking soliton equation describes the interaction of a Riemann wave propagating along the y-axis with a long wave along the x-axis. In this paper, with the aid of symbolic computation, six kinds of new special exact soltion-like solutions of (2+1)-dimensional breaking soliton equation are obtained by using some general transformations and the further generalized projective Riccati equation method. 展开更多
关键词 松散孤波方程 广义投影Riccati函数法 孤相解 非线性 偏微分
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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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Classification of All Single Traveling Wave Solutions to (3 + 1)-Dimensional Breaking Soliton Equation 被引量:1
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作者 Yang Li 《Journal of Applied Mathematics and Physics》 2014年第4期41-45,共5页
In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All s... In order to get the exact traveling wave solutions to nonlinear partial differential equation, the complete discrimination system for polynomial and direct integral method are applied to the considered equation. All single traveling wave solutions to the equation can be obtained. As an example, we give the solutions to (3 + 1)-dimensional breaking soliton equation. 展开更多
关键词 The Nonlinear Partial Differential equation Complete Discrimination System for Polynomial Direct Integral Method TRAVELING Wave Transform (3 + 1)-dimensional breaking soliton equation
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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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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
在这份报纸,(2 + 1 ) 维的 soliton 方程主要正在被讨论。把直接方法, Wronskian 技术和 Pfaffian 基于 Hirota 性质, N-soliton 答案, Wronskian 和 Grammian 答案被产生了。
关键词 孤子方程 直接方法 孤子解
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Multisoliton Solutions of the (2+1)-Dimensional KdV Equation 被引量:1
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作者 ZHANG Jie-Fang HUANG Wen-Hua 《Communications in Theoretical Physics》 SCIE CAS CSCD 2001年第11期523-524,共2页
Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2+1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear... Using the extension homogeneous balance method,we have obtained some new special types of soliton solutions of the (2+1)-dimensional KdV equation.Starting from the homogeneous balance method,one can obtain a nonlinear transformation to simple (2+1)-dimensional KdV equation into a linear partial differential equation and two bilinear partial differential equations.Usually,one can obtain only a kind of soliton-like solutions.In this letter,we find further some special types of the multisoliton solutions from the linear and bilinear partial differential equations. 展开更多
关键词 multisoliton (2+1)-dimensions KdV equation
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A Series of Variable Separation Solutions and New Soliton Structures of (2+1)-Dimensional Korteweg-de Vries Equation
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作者 XU Chang-Zhi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第3X期403-406,共4页
关键词 变量分离逼近 (2+1)维KdV方程 新孤波激发 理论物理 数学物理方法
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Painlevé Analysis,Soliton Solutions and Bcklund 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 PAINLEVÉ分析 流体力学方程 符号计算 孤子解 BACKLUND变换 转化 双线性方程 双线性形式
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Nonlocal symmetry and exact solutions of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation 被引量:3
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作者 黄丽丽 陈勇 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第6期63-70,共8页
In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the... In this paper,the truncated Painlev′e analysis,nonlocal symmetry,Bcklund transformation of the(2+1)-dimensional modified Bogoyavlenskii–Schiff equation are presented.Then the nonlocal symmetry is localized to the corresponding nonlocal group by the prolonged system.In addition,the(2+1)-dimensional modified Bogoyavlenskii–Schiff is proved consistent Riccati expansion(CRE) solvable.As a result,the soliton–cnoidal wave interaction solutions of the equation are explicitly given,which are difficult to find by other traditional methods.Moreover figures are given out to show the properties of the explicit analytic interaction solutions. 展开更多
关键词 2+1)-dimensional modified Bogoyavlenskii–Schiff equation nonlocal symmetry consistent Riccati expansion soliton–cnoidal wave solution
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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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New Multiple Soliton-like and Periodic Solutions for (2+l)-Dimensional Canonical Generalized KP Equation with Variable Coefficients 被引量:3
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作者 ZHANG Li-Hua LIU Xi-Qiang BAI Cheng-Lin 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第5X期793-798,共6页
关键词 变量系数3维规范广义方程 双曲正切函数法 类孤立子周期解 RICCATI方程
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Chirped Waves for a Generalized (2 + 1)-Dimensional Nonlinear Schrdinger Equation 被引量:1
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作者 来娴静 《Communications in Theoretical Physics》 SCIE CAS CSCD 2011年第4期555-559,共5页
The exact chirped soliton-like and quasi-periodic wave solutions of (2+1)-dimensional generalized nonlinearSchrodinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detail... The exact chirped soliton-like and quasi-periodic wave solutions of (2+1)-dimensional generalized nonlinearSchrodinger equation including linear and nonlinear gain (loss) with variable coefficients are obtained detailedly in thispaper.The form and the behavior of solutions are strongly affected by the modulation of both the dispersion coefhcientand the nonlinearity coefficient.In addition,self-similar soliton-like waves precisely piloted from our obtained solutionsby tailoring the dispersion and linear gain (loss). 展开更多
关键词 非线性薛定谔方程 广义 啁啾 非线性增益 非线性方程 非线性系数 周期波解 孤子波
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An Extended Subequation Rational Expansion Method and Solutions of (2+1)-Dimensional Cubic Nonlinear Schr(?)dinger Equation
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作者 GUO Wei-Ming~1 LI Biao~(1,3)and CHEN Yong~(1,2,3)~1 Nonlinear Science Center and Department of Mathematics,Ningbo University,Ningbo 315211,China~2 Institute of Theoretical Computing,East China Normal University,Shanghai 200062,China~3 Key Laboratory of Mathematics Mechanization,the Chinese Academy of Sciences,Beijing 100080,China 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第12期987-992,共6页
An extended subequation rational expansion method is presented and used to construct some exact,analyt-ical solutions of the (2+1)-dimensional cubic nonlinear Schrdinger equation.From our results,many known solutionso... An extended subequation rational expansion method is presented and used to construct some exact,analyt-ical solutions of the (2+1)-dimensional cubic nonlinear Schrdinger equation.From our results,many known solutionsof the (2+1)-dimensional cubic nonlinear Schrdinger equation can be recovered by means of some suitable selections ofthe arbitrary functions and arbitrary constants.With computer simulation,the properties of new non-travelling waveand coefficient function's soliton-like solutions,and elliptic solutions are demonstrated by some plots. 展开更多
关键词 (2+1)-d cubic nonlinear Schrdinger equation soliton solution elliptic function soltuions
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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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A novel(2+1)-dimensional integrable KdV equation with peculiar solution structures
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作者 楼森岳 《Chinese Physics B》 SCIE EI CAS CSCD 2020年第8期176-181,共6页
The celebrated(1+1)-dimensional Korteweg de-Vries(KdV)equation and its(2+1)-dimensional extension,the Kadomtsev-Petviashvili(KP)equation,are two of the most important models in physical science.The KP hierarchy is exp... The celebrated(1+1)-dimensional Korteweg de-Vries(KdV)equation and its(2+1)-dimensional extension,the Kadomtsev-Petviashvili(KP)equation,are two of the most important models in physical science.The KP hierarchy is explicitly written out by means of the linearized operator of the KP equation.A novel(2+1)-dimensional KdV extension,the cKP3-4 equation,is obtained by combining the third member(KP3,the usual KP equation)and the fourth member(KP4)of the KP hierarchy.The integrability of the cKP3-4 equation is guaranteed by the existence of the Lax pair and dual Lax pair.The cKP3-4 system can be bilinearized by using Hirota's bilinear operators after introducing an additional auxiliary variable.Exact solutions of the cKP3-4 equation possess some peculiar and interesting properties which are not valid for the KP3 and KP4 equations.For instance,the soliton molecules and the missing D'Alembert type solutions(the arbitrary travelling waves moving in one direction with a fixed model dependent velocity)including periodic kink molecules,periodic kink-antikink molecules,few-cycle solitons,and envelope solitons exist for the cKP3-4 equation but not for the separated KP3 equation and the KP4 equation. 展开更多
关键词 (2+1)-dimensional KdV equations Lax and dual Lax pairs soliton and soliton molecules D’Alembert type waves
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Bifurcation of travelling wave solutions for (2+1)-dimension nonlinear dispersive long wave equation
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作者 RONG Ji-hong TANG Sheng-qiang School of Mathematics and Computing Science,Guilin University of Electronic Technology,Guilin541004,China 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2009年第3期291-297,共7页
In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for (2+1)-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurca... In this paper,the bifurcation of solitary,kink,anti-kink,and periodic waves for (2+1)-dimension nonlinear dispersive long wave equation is studied by using the bifurcation theory of planar dynamical systems.Bifurcation parameter sets are shown,and under various parameter conditions,all exact explicit formulas of solitary travelling wave solutions and kink travelling wave solutions and periodic travelling wave solutions are listed. 展开更多
关键词 solitary wave kink and anti-kink wave periodic wave 2+1)-dimension nonlinear dispersive long wave equation
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New Exact Solutions for the Generalized (2 + 1)-dimensional Nonlinear Schroedinger Equation with Variable Coefficients
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作者 JIANG Zhi-ping 《Chinese Quarterly Journal of Mathematics》 CSCD 2012年第2期224-231,共8页
With the help of the variable-coefficient generalized projected Ricatti equation expansion method,we present exact solutions for the generalized(2+1)-dimensional nonlinear Schrdinger equation with variable coefficie... With the help of the variable-coefficient generalized projected Ricatti equation expansion method,we present exact solutions for the generalized(2+1)-dimensional nonlinear Schrdinger equation with variable coefficients.These solutions include solitary wave solutions,soliton-like solutions and trigonometric function solutions.Among these solutions,some are found for the first time. 展开更多
关键词 (2+1)-dimensions nonlinear Schrodinger equation variable coefficients projected Ricatti equation expansion method
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Further Extended Jacobi Elliptic Function Rational Expansion Method and New Families of Jacobi Elliptic Function Solutions to (2+1)-Dimensional Dispersive Long Wave Equation
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作者 ZHANG Yuan-Yuan WANG Qi ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第2期199-206,共8页
在这篇论文,一个进一步扩大的 Jacobi 椭圆形的函数合理扩大方法为由做更一般的转变构造非线性的部分微分方程的准确答案的新形式被建议。为说明,我们把方法用于(2+1 ) 维的散长波浪方程并且成功地获得许多新二倍地周期的答案。什么... 在这篇论文,一个进一步扩大的 Jacobi 椭圆形的函数合理扩大方法为由做更一般的转变构造非线性的部分微分方程的准确答案的新形式被建议。为说明,我们把方法用于(2+1 ) 维的散长波浪方程并且成功地获得许多新二倍地周期的答案。什么时候模量 m → 1,这些答案作为 soliton 答案堕落。方法能也被用于另外的非线性的部分微分方程。 展开更多
关键词 JACOBI椭圆函数 有理扩展法 色散长波方程 非线性偏微分方程
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