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| 內容簡介： |
《非线性波方程行波解研究：基于动力系统方法：英文》旨在让读者了解和掌握怎样从动力系统理论的角度来理解和研究非线性波方程的精确解的求解方法，以及相应的动力学特征，并利用计算机符号代数的方法和相图分析的方法给出不同波方程可能存在的行波解的种类，分析这些复杂行波解产生的原因，以及从广义解的角度理解各种非光滑行波解思路。來源：香港大書城megBookStore,http://www.megbook.com.hk
《非线性波方程行波解研究：基于动力系统方法：英文》可供高等学校数学、物理和力学专业高年级学生及研究生阅读，还可作为相关专业教师及研究人员的参考书。
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| 目錄：
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Chapter 1 Basic Mathematical Theory of the Traveling Wave System 1
1.1 Dynamical Systems andNonlinear WaveEquations 1
1.2 Research Methods for Singular TravelingWave Systems 4
1.3 Introduction to GeometricSingularPerturbationTheory 6
Chapter 2 Bifurcations of Traveling Wave Solutions for the Combined KdV—MKdV Equation 9
2.1 Bifurcations of Phase Portraits of System(2.0.6) 10
2.2 Solitary Wave and Kink Wave Solutions 21
2.3 Smooth Traveling Wave Solutions and Exact Solution Formulas 24
Chapter 3 Bifurcations of Traveling Wave Solutions for the Generalized Compound KdV Equations 27
3.1 Bifurcations of Phase Portraits of System (3. 0. 6) When p Is Odd 28
3.2 Bifurcations of Phase Portraits of System (3. 0. 6) When p Is Even 26
Chapter 4 Exact Traveling Wave Solutions for the Benjamin — Bona— Mahony Equation 43
4.1 Introduction 43
4.2 Description of the Improved Fan Sub-equationMethod 44
4.3 Exact Solutions to the BBM Equation 45
4.4 Conclusion 57
Chapter 5 Single Peak Solitary Wave Solutions for the Variant Boussinesq Equations 59
5.1 Asymptotic Behavior of Solutions 60
5.2 Smooth and Cusped Single Peak Solitary WaveSolutions 63
Chapter 6 Single Peak Solitary Wave Solutions for the Generalized Camassa—Holm Equation 73
6.1 Asymptotic Behavior of Solutions 75
6.2 Smooth， Peaked and Cusped Single Peak Solitary Wave Solutions 79
Chapter 7 Single Peak Solitary Wave Solutions for the Generalized Korteweg— de Vries Equation 90
7.1 Asymptotic Behavior of Solutions 91
7.2 Smooth， Peaked and Cusped Single Peak Solitary Wave Solutions 96
Chapter 8 Compacton-Iike Solutions in a Camassa —Holm Type Equation 107
8.1 Hamiltonian System and Newton Equation 108
8.2 Phase —Space AnalysisofCompacton-like Solutions 110
Chapter 9 Solitary Wave and Chaotic Behavior for the Coupled Schrodinger—KdV Equations 114
9.1 The Exact Explicit Solitary Wave Solution and Periodic Wave So-lutions Determined bySystem(9.0.3) 115
9.2 The Chaotic Behavior of Traveling Wave Solutions Defined by Equation (9.0.4) 119
Chapter 10 Solitary Waves and Periodic Waves in a Perturbed KdV Equation 124
10.1 Introduction to the PerturbedKdVEquation 124
10.2 Perturbation Analysis 128
10.3 Analysis by the AbelianIntegralTheory 132
10.4 Main Results 137
Bibliography 143
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