位置：成果数据库 > 期刊 > 期刊详情页
一个可积非线性演化方程的达布变换及其精确解
  • ISSN号：1671-6841
  • 期刊名称：Journal of Zhengzhou University
  • 时间：2012
  • 页码：31-34
  • 分类：O175.29[理学—数学;理学—基础数学]
  • 作者机构：[1]商丘师范学院数学系,河南商丘476000, [2]郑州大学数学系,河南郑州450001
  • 相关基金：国家自然科学基金资助项目,编号11171312,11001250.
  • 相关项目：谱变换在非线性可积方程初边值问题中的应用
作者： 马云苓|曾昕|耿献国|
关键词： 非线性演化方程, 达布变换, 精确解, nonlinear evolution equation, Darboux transformation, exact solution
中文摘要：

研究了一个新的可积非线性演化方程,基于其Lax对和谱问题的规范变换,构造出该方程的一个达布变换,进而利用此达布变换,得到该方程的精确解,包括有理解、孤子解与周期解.

英文摘要：

A new integrable nonlinear evolution equation was proposed. Based on the resulting Lax pair,a Darboux transformation of the nonlinear evolution equation was structured with the aid of the gauge transformation, by which some exact solutions of the nonlinear evolution equation were obtained, inclu- ding rational solutions, soliton solutions and periodic solutions.

同期刊论文项目
谱变换在非线性可积方程初边值问题中的应用
期刊论文 11
三角曲线与孤子方程的代数几何解
期刊论文 52
同项目期刊论文
Conservation Laws and Darboux Transformation for Sharma-Tasso-Olver Equation
N-soliton and quasi-periodic solutions of the KdV6 equations
Algebro-geometric solutions to the modified Sawada-Kotera hierarchy
Initial-boundary value problems for the coupled nonlinear Schrodinger equation on the half-line
Explicit quasi-periodic solutions of the Kaup-Newell hierarchy
Explicit solutions for a hierarchy of differential-difference equations
Explicit quasi-periodic solutions of the Vakhnenko equation
Quasi-periodic solutions to the two-component nonlinear Klein-Gordon equation
On the application ofa generalized version of the dressing method to the integration of variablecoef
A super hierarchy of the vector nonlinear Schrodinger equations and Hamiltonian structures, conserva
New Wronskian Representation of Solution for a Variable-Coefficient Kadomtsev-Petviashvili Equation
The full positive flows of Manakov hierarchy, Hamiltonian structures and conservation laws
Quasi-Periodic Solutions of Coupled KDV Type Equations
Quasi-periodicsolutions of the discrete mKdV hierarchy
The partial derivative-Dressing Method for the Sasa-Satsuma Equation with Self-Consistent Sources
A Variable-Coefficient Manakov Model and Its Explicit Solutions through the Generalized Dressing Met
Coupled Camassa-Holm equations, N-peakons and infinitely many conservation laws
Quasi-periodic solutions ofthe relativistic Toda hierarchy
Quasi-periodic Solutions of the Kaup-Kupershmidt Hierarchy
Algebro-geometric quasi-periodic solutions to the three-wave resonant interaction hierarchy &nbs
Quasiperiodic solutions of the discrete Chen-Lee-Liu hierarchy
Algebro-geometric solutions of the discrete Ragnisco-Tu hierarchy  
A novel hierarchy of differential-integral equations and their generalized bi-Hamiltonian structures
A super hierarchy of coupled derivative nonlinear Schrodinger equations and conservation laws
Novel Wronskian Condition and New Exact Solutions to a (3+1)-Dimensional Generalized KP Equation
A hierarchy of new nonlinear evolution equations and their bi-Hamiltonian structures
Exact quasi-periodic solutions of the Konno-Oono equations
Algebro-geometricconstructions of quasi- periodic flows of the discrete self-dual network hierarchy
New hierarchy of integrable nonlinear differential-difference equations
Algebro-geometricsolutions to a new hierarchy of soliton equations
A hierarchy of new nonlinear evolution equations and generalized bi-Hamiltonian structures
Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions
A note on the quasi-periodic solutions of the modified Boussinesq hierarchy
An integrable extension of TD hierarchy and generalized bi-Hamiltonian structures
A new integrable equation with peakons and cuspons and its bi-Hamiltonian structure
Algebro-geometric solution to the Bullough-Dodd-Zhiber-Shabat equation
 Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy
Straightening out of the flows for the Hu hierarchy and its algebro-geometric solutions
A super Camassa-Holm equation with N-peakon solutions
A generalization of Toda lattices and their bi-Hamiltonian structures
Darboux and Backlund transformations of the bidirectional Sawada-Kotera equation
混合Boussinesq方程的有限亏格解
Darboux transformation for an integrable generalization of the nonlinear Schrodinger equation
An extension of the modified Sawada-Kotera equation and conservation laws
（2＋1）-维耦合的mKP方程的代数几何解
The AB equations and the Dbar-dressing method in semi-characteristic coordinates
A New Solution to the Hirota-Satsuma Coupled KdV Equations by the Dressing Method
Algebro-Geometric Solutions of the TD Hierarchy
The Dbar-dressing Method for the Sasa-Satsuma Equation with Self-Consistent Sources
Coupled Nonlinear Schrodinger Equations and the Miura Transformation
DRESSING METHOD FOR A GENERALIZED FOCUSING NLS EQUATION VIA LOCAL RIEMANN-HILBERT PROBLEM
Davey-Stewartson 类方程和穿衣服方法
A hierarchy of coupled evolution equations with self-consistent sources and the dressing method
The Mikhauilov-Novikov-Wang Hierarchy and Its Hamiltonian Structures
Dbar-problem and Cauchy matrix for the mKdV equation with self-consistent sources
期刊信息
  • 《郑州大学学报：理学版》
  • 中国科技核心期刊
  • 主管单位:河南省教育厅
  • 主办单位:郑州大学
  • 主编：李燕燕
  • 地址：郑州市高新区科学大道100号
  • 邮编：450001
  • 邮箱：lixueban@zzu.edu.cn
  • 电话：0371-67781272
  • 国际标准刊号：ISSN：1671-6841
  • 国内统一刊号：ISSN：41-1338/N
  • 邮发代号:36-191
  • 获奖情况:
  • 国内外数据库收录:
  • 美国化学文摘（网络版）,美国数学评论（网络版）,波兰哥白尼索引,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,英国英国皇家化学学会文摘
  • 被引量:2791