位置：成果数据库 > 期刊 > 期刊详情页
两非线性波方程真圈解的存在性和破缺性质
  • ISSN号：1000-0887
  • 期刊名称：《应用数学和力学》
  • 时间：0
  • 分类：O357.1[理学—流体力学;理学—力学]
  • 作者机构：[1]浙江师范大学数学系,浙江金华321004, [2]昆明理工大学理学院,昆明650093
  • 相关基金：国家自然科学基金资助项目（10671179,10831003）
作者： 李继彬[1,2]
关键词： 破缺波解, 精确圈解, 非线性波方程, 平面动力系统, breaking wave solution, loop-solution, nonlinear wave equation, planar dynamical system
中文摘要：

对于某些非线性波方程，动力系统方法的分析说明所谓的圈孤子解和反圈孤子解实际上是人为的现象．所谓的圈孤子解由3个解合成，不是1个真解．是否存在非线性波方程，使得该方程的行波系统存在真正的1个圈解？若这样的解存在，它们有怎样的精确参数表示？该文回答这些问题．

英文摘要：

Dynamical analysis revealed that for some nonlinear wave equations, loop- and inverted loop-soliton solutions are merely visual artifacts. So called loop-soliton solution consists of three solutions which is not one real solution. Whether or not them exist some nonlinear wave equations for which there exists a ＂real＂ loop-solution？ If yes, what are their precise parametric representations of these loop traveling wave solutions？ These problems are answered.

同期刊论文项目
常微分方程与动力系统的分支理论和应用
期刊论文 100
非线性波研究的动力系统方法和等变全局分支
期刊论文 25 著作 1
同项目期刊论文
Dynamical understanding of loop soliton solution for several nonlinear wave equations
On a class of singular nonlinear traveling wave equations
Chaotic motion and Hamiltonian dynamics of a pre-stressed incompressible elastic plate due to resona
Breaking Wave Solutions to the Second Class of Singular Nonlinear Traveling Wave Equations
Exact Solutions and Their Dynamics of Traveling Waves in Three Typical Nonlinear Wave Equations
Center problem and multiple Hopf bifurcation for the Z5_equivariant planar polynomial vector fields
Center problem and multiple Hopf bifurcation for the Z6_equivariant planar polynomial vector fields
Exact Explicit Peakon and Periodic Cusp Wave Solutions for Several Nonlinear Wave Equations
Existence and breaking property of real loop-solutions of two nonlinear wave equations
Bifurcations of travelling wave solutions for two generalized Boussinesq systems
New study on the center problem and bifurcations of limit cycles for the Lyapunov system(II),19(9),
On a Class of Singular Nonlinear Traveling Wave Equations (II): an Example of GCKdV Equations
On the Study of Singular Nonlinear TravelingWave Equations: Dynamical System Approach
Singular Point Values, Center Problem and Bifurcations of Limit Cycles of Two Dimensional Differenti
（2＋1）-维广义Benney—Luke方程的精确行波解
M．Wadati可积非线性发展方程的精确行波解
Exact traveling wave solutions for an integrable nonlinear evolution equation given by M. Wadati
Kink wave determined by parabola solution of a nonlinear ordinary differential equation
Exact traveling wave solutions to 2D-generalized Benney-Luke equation
Existence and breaking property of real loop-solutions of two nonlinear wave equations
两分量Bose-Einstein凝聚态系统的混沌与分支
某一类控制系统中发生的指数偏差现象
Extreme Growth Rates of Periodic Orbits in Flows
Riemann theta function periodic wave solutions for the variable- coefficient mKdV equation
Integrable discretizations and soliton solution of KdV and mKdV equations
Exact travelling wave solutions to two integrable KdV6 equations
Exact solitary wave and quasiperiodic wave solutions for four fifthorder nonlinear wave equations
Exact traveling wave solutions and bifurcations in a nonlinear elastic rod equation
A new Chebyshev family with applications to Abel equations
A note on “The integrable KdV6 equation: Multiple soliton solutions and multiple singular soliton so
Exact Travelling Wave Solutions and Their Bifurcations for the KudryashovSinelshchikov Equation
Metric entropy and the number of periodic points
On the travelling wave solutions for a nonlinear diffusionconvection equation: dynamical system appr
Lyapuniv exponents of hyperbolic measures and hyperbolic periodic orbits
A multiple exp- function method for nonlinear differential equations and its application
Hirota bilinear equations with linear subspaces of solutions
Exact heteroclinic cycle family and quasi-periodic solutions for the three-dimensional systems deter
Bifurcations and exact travelling wave solutions of the generalized twocomponent CamassaHolm equatio
Generalized Wronskian solutions for the (3 + 1)-dimensional Jimbo– Miwa equation
Uniqueness of limit cycles for Li\'enard differential equations of degree four
Knotted periodic solutions of a linear non-autonomous system and some related three- dimensional flo
Abelian integrals and limit cycles
Wronskian and Grammian Solutions for (2 + 1)-Dimensional Soliton Equation
Korteweg–de Vries Equation (KdV), History, Exact N- Soliton Solutions and Further Properties
Zero entropy versus infinite entropy
On the Hopf-zero bifurcation of the Michelson system
Homoclinic manifolds, center manifolds and exact solutions of fourdimensional travelling wave system
The embedding flows of C^\infty hyperbolic diffeomorphisms
Explicit soliton solutions of the Kaup-Kupershmidt equation through the dynamical system approach
Generalized rational first integrals of analytic differential systems
Bifurcation in a ratio-dependent predator-prey model with prey harvesting
The 16th Hilbert problem on algebraic limit cycles, Journal of Differential Equations
Global structure of quaternion polynomial differential equations
Solitary wave and chaotic behavior of travelling wave solutions for the coupled KdV equations
On nonlinear wave equations with breaking loop-solutions
Embedding smooth diffeomorphisms in flows
Soliton resonance of the NI-BKP equation
Non-uniformly hyperbolic periodic points and uniform hyperbolicity for $C^1$diffeomorphisms
New results on the study of $Z_q$-equivariant planar polynomial vector fields
Quadratic Perturbations of a Quadratic Reversible Lotka-Volterra System,
Bifurcations of traveling wave solutions of an integrable equation
Bifurcations and parametric representations of traveling wave solutions for the $(2+1)-$dimensional
On Dirac physical measures for transitive flows
Exact Dark Soliton, Periodic Solutions and Chaotic Dynamics in a Perturbed Generalized Nonlinear Sch
B?cklund transformations and soliton solutions for the KdV6 equation
Exact homoclinic orbits and heteroclinic families for the thirdorder system given by Chazy XI (N=3)
The exact bounds on the number of zeros of complete hyperelliptic integrals of the ?rst kind
Exact M/W-shape wave solutions determined by a singular traveling wave equation
Approximation properties on invariant measure and Oseledec splitting in non-hyperbolic systems
Exact dark soliton solution of the generalized nonlinear Schrdinger equation
Family of nonlinear wave equations which yield loop solutions and solitary wave solutions
On the Breaking Property for the Second Class of Singular Nonlinear Traveling Wave Equations
Limit cycles of differential systems via the averaging methods
Chaotic motion and Hamiltonian dynamics of a prestressed incompressible elastic plate due to resonan
A class of exact solutions of the generalized nonlinear Schrodinger equation
Exact loop solution,cusp solutions, solitary wave solutions and periodic wave solutions for the spec
The cyclicity of period annulus of a quadratic reversible Lotka-Volterra system, Nonlinearity
Resonance of solitons in a coupled higher-order Ito equation
Bounded complexity function versus unbounded complexity function
Canard Limit Cycles for Predator-Prey Systems with Holling Types of Functional Response
Exact Travelling Wave Solutions and Their Bifurcations for the generalized PochhammerChree equations
Exact solutions and Painlevé analysis of a new (2+1)- dimensional generalized KdV equation
Lower bounds for the Hilbert number of polynomial systems
Exstence of exact families of travelling wave solutions for the sixth-order Ramani equation and coup
Darboux polynomials and rational first integrals of the generalized Lorenz systems
Dominated splittings and Pesin formula
Deviation property of periodic measures in C1 nonuniformly hyperbolic systems with limit domination
Existence and breaking property of real loop-solutions of two nonlinear wave equations
The Travelling Wave Solutions for （2＋1）-dimensional AKNS Equation
弱化希尔伯特第16问题及其研究现状
Binary Bell polynomial application in generalized （2＋1）-dimensional KdV equation with variable coefficients
Riemann theta function periodic wave solutions for the variable-coefficient mKdV equation
EXACT DARK SOLITON AND ITS PERSISTENCE IN THE PERTURBED （2＋1）-DIMENSIONAL DAVEY-STEWARTSON SYSTEM
期刊信息
  • 《应用数学和力学》
  • 中国科技核心期刊
  • 主管单位:重庆交通大学
  • 主办单位:重庆交通大学
  • 主编：钟万勰
  • 地址：重庆南岸区重庆交通大学90信箱
  • 邮编：400074
  • 邮箱：applmathmech@cqjtu.edu.cn
  • 电话：023-62652450
  • 国际标准刊号：ISSN：1000-0887
  • 国内统一刊号：ISSN：50-1060/O3
  • 邮发代号:78-21
  • 获奖情况:
  • 国际工程索引（EI）收录期刊,我国力学类核心期刊,中国期刊方阵“双效”期刊
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,日本日本科学技术振兴机构数据库,美国应用力学评论,中国中国科技核心期刊,中国北大核心期刊（2004版）,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）,中国北大核心期刊（2000版）
  • 被引量:8965