期刊文献+
共找到115篇文章
< 1 2 6 >
每页显示 20 50 100
An integrable generalization of the Fokas–Lenells equation:Darboux transformation, reduction and explicit soliton solutions
1
作者 魏姣 耿献国 王鑫 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第7期117-124,共8页
Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge t... Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically. 展开更多
关键词 darboux transformation soliton solutions generalized Fokas–Lenells equation
下载PDF
Darboux transformation,infinite conservation laws,and exact solutions for the nonlocal Hirota equation with variable coefficients
2
作者 刘锦洲 闫鑫颖 +1 位作者 金梦 辛祥鹏 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期263-269,共7页
This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructe... This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations. 展开更多
关键词 infinite conservation laws nonlocal Hirota equation with variable coefficient soliton solutions darboux transformation
下载PDF
Darboux Transformation and Explicit Solutions for Discretized Modified Korteweg-de Vries Lattice Equation 被引量:9
3
作者 闻小永 高以天 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第5期825-830,共6页
The modified Korteweg-de Vries (mKdV) typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With th... The modified Korteweg-de Vries (mKdV) typed equations can be used to describe certain nonlinear phenomena in fluids, plasmas, and optics. In this paper, the discretized mKdV lattice equation is investigated. With the aid of symbolic computation, the discrete matrix spectral problem for that system is constructed. Darboux transformation for that system is established based on the resulting spectral problem. Explicit solutions are derived via the Darboux transformation. Structures of those solutions are shown graphically, which might be helpful to understand some physical processes in fluids, plasmas, and optics. 展开更多
关键词 darboux transformation discretized modified Korteweg-de Vries lattice equation explicit solutions symbolic computation
下载PDF
Darboux Transformations and Soliton Solutions for Classical Boussinesq-Burgers Equation 被引量:4
4
作者 XU Rui 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第9期579-582,共4页
Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgersequation are presented in this letter.They are used to generate new solutions of the classical Boussinesq-Burgerseq... Two basic Darboux transformations of a spectral problem associated with a classical Boussinesq-Burgersequation are presented in this letter.They are used to generate new solutions of the classical Boussinesq-Burgersequation. 展开更多
关键词 classical Boussinesq-Burgers equation darboux transformation soliton solution
下载PDF
Darboux Transformation and Explicit Solutions for Drinfel'd-Sokolov-Wilson Equation 被引量:4
5
作者 耿献国 吴丽华 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第6期1090-1096,共7页
A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spect... A generalized Drinfel'd Sokolov-Wilson (DSW) equation and its Lax pair are proposed. A Daorboux transformation for the generalized DSW equation is constructed with the help of the gauge transformation between spectral problems, from which a Darboux transformation for the DSW equation is obtained through a reduction technique. As an application of the Darboux transformations, we give some explicit solutions of the generalized DSW equation and DEW equation such as rational solutions, soliton solutions, periodic solutions. 展开更多
关键词 Drinfel'd-Sokolov-Wilson equation darboux transformation explicit solutions
下载PDF
AUTO-DARBOUX TRANSFORMATION AND EXACT SOLUTIONS OF THE BRUSSELATOR REACTION DIFFUSION MODEL 被引量:3
6
作者 YAN Zhenya(闫振亚) +1 位作者 ZHANG Hongqing(张鸿庆) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第5期541-546,共6页
Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain ... Firstly, using the improved homogeneous balance method, an auto-Darboux transformation (ADT) for the Brusselator reaction diffusion model is found. Based on the ADT, several exact solutions are obtained which contain some authors' results known. Secondly, by using a series of transformations, the model is reduced into a nonlinear reaction diffusion equation and then through using sine-cosine method, more exact solutions are found which contain soliton solutions. 展开更多
关键词 brusselator reaction model darboux transformation homogeneous balance method sine-cosine method exact solution
下载PDF
Darboux Transformations for Space-Like Isothermic Surfaces in R^m,1 被引量:4
7
作者 ZUODa-Feng CHENQing CHENGYi 《Communications in Theoretical Physics》 SCIE CAS CSCD 2004年第6期816-820,共5页
In this paper,by using the G_(m,1)~(1,1)-system,we study Darboux transformations for space-like isothermic surfaces in Minkowski space R~(m,1),where G_(m,1)~(1,1)=O(m+1,2)/O(m,1)×O(1,1).
关键词 G_(m 1)~(1 1)-system darboux transformation space-like isothermic surfaces
下载PDF
DARBOUX TRANSFORMATION OF A NONLINEAR EVOLUTION EQUATION AND ITS EXPLICIT SOLUTIONS 被引量:2
8
作者 李文敏 韩有攀 周高军 《Acta Mathematica Scientia》 SCIE CSCD 2011年第4期1457-1464,共8页
In this paper, we study a differential-difference equation associated with discrete 3 × 3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-... In this paper, we study a differential-difference equation associated with discrete 3 × 3 matrix spectral problem. Based on gauge transformation of the spectral problm, Darboux transformation of the differential-difference equation is given. In order to solve the differential-difference equation, a systematic algebraic algorithm is given. As an application, explicit soliton solutions of the differential-difference equation are given. 展开更多
关键词 darboux transformation SOLITONS explicit solution Lax-pair differentialdifference equation
下载PDF
Lax Pair and Darboux Transformation for a Variable-Coefficient Fifth-Order Korteweg-de Vries Equation with Symbolic Computation 被引量:2
9
作者 ZHANG Ya-Xing ZHANG Hai-Qiang +3 位作者 LI Juan XU Tao ZHANG Chun-Yi TIAN Bo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2008年第4期833-838,共6页
In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering ... In this paper, we put our focus on a variable-coe^cient fifth-order Korteweg-de Vries (fKdV) equation, which possesses a great number of excellent properties and is of current importance in physical and engineering fields. Certain constraints are worked out, which make sure the integrability of such an equation. Under those constraints, some integrable properties are derived, such as the Lax pair and Darboux transformation. Via the Darboux transformation, which is an exercisable way to generate solutions in a recursive manner, the one- and two-solitonic solutions are presented and the relevant physical applications of these solitonic structures in some fields are also pointed out. 展开更多
关键词 variable-coefficient fifth-order Korteweg-de Vries equation Lax pair darboux transformation solitonic solutions symbolic computation
下载PDF
Solving Kadomtsev—Petviashvili Equation via a New Decomposition and Darboux Transformation 被引量:2
10
作者 FANEn-Gui 《Communications in Theoretical Physics》 SCIE CAS CSCD 2002年第2期145-148,共4页
Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a ... Recently, a new decomposition of the -dimensional Kadomtsev?Petviashvili (KP) equation to a -dimensional Broer?Kaup (BK) equation and a -dimensional high-order BK equation was presented by Lou and Hu. In our paper, a unified Darboux transformation for both the BK equation and high-order BK equation is derived with the help of a gauge transformation of their spectral problems. As application, new explicit soliton-like solutions with five arbitrary parameters for the BK equation, high-order BK equation and KP equation are obtained. 展开更多
关键词 KP equation BK equation darboux transformation exact solution
下载PDF
Darboux transformation and soliton solutions of a nonlocal Hirota equation 被引量:1
11
作者 Yarong Xia Ruoxia Yao Xiangpeng Xin 《Chinese Physics B》 SCIE EI CAS CSCD 2022年第2期242-249,共8页
Starting from local coupled Hirota equations,we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz–Kaup–Newell–Segur scattering problem.The Lax integrabilit... Starting from local coupled Hirota equations,we provide a reverse space-time nonlocal Hirota equation by the symmetry reduction method known as the Ablowitz–Kaup–Newell–Segur scattering problem.The Lax integrability of the nonlocal Hirota equation is also guaranteed by existence of the Lax pair.By Lax pair,an n-fold Darboux transformation is constructed for the nonlocal Hirota equation by which some types of exact solutions are found.The solutions with specific properties are distinct from those of the local Hirota equation.In order to further describe the properties and the dynamic features of the solutions explicitly,several kinds of graphs are depicted. 展开更多
关键词 nonlocal Hirota equation darboux transformation Lax pair soliton soultion
下载PDF
Hamiltonian Systems and Darboux Transformation Associated with a 3 × 3 Matrix Spectral Problem 被引量:1
12
作者 LUO Lin FAN En-Gui 《Communications in Theoretical Physics》 SCIE CAS CSCD 2007年第2X期205-210,共6页
Starting from a 3 × 3 matrix spectral problem, we derive a hierarchy of nonlinear equations. It is shown that the hierarchy possesses bi-Hamiltonian structure. Under the symmetry constraints between the potential... Starting from a 3 × 3 matrix spectral problem, we derive a hierarchy of nonlinear equations. It is shown that the hierarchy possesses bi-Hamiltonian structure. Under the symmetry constraints between the potentials and the eigenfunctions, Lax pair and adjoint Lax pairs including partial part and temporal part are nonlinearied into two finitedimensional Hamiltonian systems (FDHS) in Liouville sense. Moreover, an explicit N-fold Darboux transformation for CDNS equation is constructed with the help of a gauge transformation of the spectral problem. 展开更多
关键词 nonlinear equations Hamiltonian system symmetry constraint darboux transformation
下载PDF
Darboux Transformation for Tzitzeica Equation 被引量:1
13
作者 ZHU Jun-Yi GENG Xian-Guo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第4期577-580,共4页
We present a Darboux transformation for Tzitzeica equation associated with 3 × 3 matrix spectral problem.The explicit solution of Tzitzeica equation is obtained,
关键词 darboux transformation nonlinear evolution equation soliton solutions
下载PDF
Darboux Transformation and New Soliton-like Solutions for (1+1)-Dimensional Higher-Order Broer-Kaup System 被引量:1
14
作者 YU Rui HUANG Ding-Jiang ZHANG Hong-Qing 《Communications in Theoretical Physics》 SCIE CAS CSCD 2006年第3期401-404,共4页
In this letter, we construct a kind of new Darboux transformation for the (1+1)-dimensional higher-order Broer-Kaup (HBK) system with the help of a gauge transformation of a spectral problem. By applying this new... In this letter, we construct a kind of new Darboux transformation for the (1+1)-dimensional higher-order Broer-Kaup (HBK) system with the help of a gauge transformation of a spectral problem. By applying this new Darboux transformation, some new soliton-like solutions of the (1+1)-dimensional HBK system are obtained. 展开更多
关键词 darboux transformation (1+1)-dimensional higher-order Broer-Kaup system soliton-like solu-tions
下载PDF
Hierarchy of Lax Integrable Lattice Equations, Darboux Transformation and Conservation Laws 被引量:1
15
作者 孙业朋 《Journal of Shanghai University(English Edition)》 CAS 2005年第6期471-475,共5页
A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of c... A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of conservation laws were given for the corresponding hierarchy. 展开更多
关键词 lattice soliton equation darboux transformation conservation law.
下载PDF
N-Fold Darboux Transformation for the Nonlocal Nonlinear Schrodinger(NNLS)Equation with the Self-Induced PT-Symmetric Potential 被引量:2
16
作者 Chaonan Duan Fajun Yu 《Journal of Applied Mathematics and Physics》 2018年第4期888-900,共13页
The Darboux transformation (DT) method is studied in a lot of local equations, but there are few of work to solve nonlocal equations by DT. In this letter, we solve the nonlocal nonlinear Schr&#246;dinger equation... The Darboux transformation (DT) method is studied in a lot of local equations, but there are few of work to solve nonlocal equations by DT. In this letter, we solve the nonlocal nonlinear Schr&#246;dinger equation (NNLSE) with the self-induced PT-symmetric potential by DT. Then the N-fold DT of NNLSE is derived with the help of the gauge transformation between the Lax pairs. Then we derive some novel exact solutions including the bright soliton, breather wave soliton. In particularly, the dynamic features of one-soliton, two-soliton, three-soliton solutions and the elastic interactions between the two solitons are displayed. 展开更多
关键词 Nonlocal Nonlinear Schrodinger Equation N-Fold darboux transformation Lax Pairs Exact Solution
下载PDF
N-Fold Darboux Transformation for a Nonlinear Evolution Equation 被引量:2
17
作者 Yannan Zhao 《Applied Mathematics》 2012年第8期943-948,共6页
In this paper, we present a N-fold Darboux transformation (DT) for a nonlinear evolution equation. Comparing with other types of DTs, we give the relationship between new solutions and the trivial solution. The DT pre... In this paper, we present a N-fold Darboux transformation (DT) for a nonlinear evolution equation. Comparing with other types of DTs, we give the relationship between new solutions and the trivial solution. The DT presented in this paper is more direct and universal to obtain explicit solutions. 展开更多
关键词 darboux transformation Derivative Nonlinear Schrodinger Equation Explicit Solution
下载PDF
Darboux Transformation and Solitons for Reduced Maxwell-Bloch Equations
18
作者 JIQing-Chun 《Communications in Theoretical Physics》 SCIE CAS CSCD 2005年第6期983-986,共4页
The Darboux transformations from arbitrary solutions of reduced Maxwell-Bloch equations is constructed in this article. Hence, in principle, we can find multi-soliton solutions by algebric algorithm, and the formula w... The Darboux transformations from arbitrary solutions of reduced Maxwell-Bloch equations is constructed in this article. Hence, in principle, we can find multi-soliton solutions by algebric algorithm, and the formula will be given explicitly. 展开更多
关键词 reduced Maxwell-Bloch equations Lax pair darboux transformations SOLITONS multi-solitons
下载PDF
Painlevé Analysis and Darboux Transformation for a Variable-Coefficient Boussinesq System in Fluid Dynamics with Symbolic Computation
19
作者 李宏哲 田播 +1 位作者 李丽莉 张海强 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第5期831-836,共6页
The new soliton solutions for the variable-coefficient Boussinesq system, whose applications are seen influid dynamics, are studied in this paper with symbolic computation. First, the Painleve analysis is used to inve... The new soliton solutions for the variable-coefficient Boussinesq system, whose applications are seen influid dynamics, are studied in this paper with symbolic computation. First, the Painleve analysis is used to investigateits integrability properties. For the identified case we give, the Lax pair of the system is found, and then the Darbouxtransformation is constructed. At last, some new soliton solutions are presented via the Darboux method. Those solutionsmight be of some value in fluid dynamics. 展开更多
关键词 variable-coefficient Boussinesq system Lax pair darboux transformation soliton solutions symbolic computation
下载PDF
N-Fold Darboux Transformation and Bidirectional Solitons for Whitham-Broer-Kaup Model in Shallow Water
20
作者 王雷 高以天 +3 位作者 盖晓玲 孟得新 吕兴 于鑫 《Communications in Theoretical Physics》 SCIE CAS CSCD 2010年第3期413-422,共10页
Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kau... Under investigation in this paper is the Whitham-Broer-Kaup (WBK) system, which describes the dispersive long wave in shallow water. Through a variable transformation, the WBK system is casted into a general Broer-Kaup system whose Lax pair can be derived by the Ablowitz-Kaup-Newell-Segur technology. With symbolic computation, based on the aforementioned Lax pair, the N-fold Darboux transformation is constructed with a gauge transformation and the multi-soliton solutions are obtained. Finally, the elastic interactions of the two-soliton solutions (including the head-on and overtaking collisions) for the WBK system are graphically studied. Those multi-soliton collisions can beused to illustrate the bidirectional propagation of the waves in shallow water. 展开更多
关键词 Whitham Broer-Kaup system Bidirectional solitons Multi-soliton solutions N-fold darboux transformation Lax pair
下载PDF
上一页 1 2 6 下一页 到第
使用帮助 返回顶部