《奇非線性行波方程研究的動力系統方法》是2007年科學出版社出版的圖書，作者是Jibin Li（李繼彬）、Huihui Dai（戴暉暉）。
基本介紹
- 中文名：奇非線性行波方程研究的動力系統方法
- 作者：Jibin Li（李繼彬）、Huihui Dai（戴暉暉）
- 類別：數學
- 出版社：科學出版社
- 出版時間：2007-04
- ISBN：9787030188359
內容簡介,圖書目錄,
內容簡介
The Studies of solitons and complete integrability of nonlinear wave equations and bifurcations and chaos of dynamical ystems are two very active fields in nonlinear science. Because a homoclinic orbit of a traveling wave system(ODEs) corresponds to a solitary wave solution of a nonlinear wave equation(PDE). This fact provides an intersection point for above two study fields. The aim of this book is to give a more systematic accotmt for the bifurcation theory method of dynamical systems to find traveling wave solutions with an emphasis on singular waves and understand their dynamics for some classes of the wellposedness of nonlinear evolution equations. Readers shall find how standard methods of the theory of dynamical systems may be used for the study of traveling wave solutions even the case of systems with discontinuities. Any reader trying to understand the subject of this book is only required to know the elementary theory of dynamical systems and elementary knowledge of nonlinear wave equations. This book should be useful as a research reference for graduate students, teachers and engineers in different study fields.
圖書目錄
Chapter 1 Traveling Wave Equations of Some Physical Models
Chapter 2 Basic Mathematical Theory of the Singular Traveling Wave Systems
Chapter 3 Bifurcations of Traveling Wave Solutions of Nonlinear Elastic Rod Systems
Chapter 4 Bifurcations of Traveling Wave Solutions of Generalized Camassa-Holm Equation
Chapter 5 Bifurcations of Traveling Wave Solutions of Higher Order Korteweg-De Vries Equations
Chapter 6 The Bifurcations of the Traveling Wave Solutions of K(m, n) Equation
Chapter 7 Kink Wave Solution Determined by a Parabola Solution of Planar Dynamical Systems
Chapter 8 Traveling Wave Solutions of Coupled Nonlinear Wave Equations
Chapter 9 Solitary Waves and Chaotic Behavior for a Class of Coupled Field Equations
Chapter 10 Bifurcations of Breather Solutions of Some Nonlinear Wave Equations
Chapter 11 Bounded Solutions of (n + 1)-Dimensional Sineand Sinh-Gordon Equations
Chapter 12 Exact Explicit Traveling Wave Solutions for Two Classes of (n + 1)-Dimensional Nonlinear Wave Equations
References
