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内容简介
浅水波，非线性光学、电磁学、等离子物理、凝聚态物理、生物及化学、通讯等领域均存在非线性波运动.对其数学模型--波方程的解研究有重要价值.上世纪90年代,数学家发现了行波方程的非光滑的孤粒子解(peakon)、有限支集解(compacton)和圈解(loopsolution)等,为理解这些解,是非光滑解的出现,导致用动力系统的分支理论及方法对奇行波方程进行研究的新方向.《平面动力系统的若干经典问题（英文版）》介绍两类奇行波方程的研究的动力系统方法,及对大量数学物理问题的应用。
目录
Preface
1 Basic Concept and Linearized Problem of Systems
1.1 Basic Concept and Variable Transformation
1.2 Resultant of the Weierstrass Polynomial and Multiplicity of a Singular Point
1.3 Quasi-Algebraic Integrals of Polynomial Systems
1.4 Cauchy Majorant and Analytic Properties in a Neighborhood of an Ordinary Point
1.5 Classification of Elementary Singular Points and Linearized Problem
1.6 Node Value and Linearized Problem of the Integer-Ratio Node
1.7 Linearized Problem of the Degenerate Node
1.8 Integrability and Linearized Problem of Weak Critical Singular Point
1.9 Integrability and Linearized Problem of the Resonant Singular Point
2 Focal Values, Saddle Values and Singular Point Values
2.1 Successor Functions and Properties of Focal Values
2.2 Poincare Formal Series and Algebraic Equivalence
2.3 Linear Recursive Formulas for the Computation of Singular Point Values
2.4 The Algebraic Construction of Singular Values
2.5 Elementary Generalized Rotation Invariants of the Cubic Systems
2.6 Singular Point Values and Integrability Condition of the Quadratic Systems
2.7 Singular Point Values and Integrability Condition of the Cubic Systems Having Homogeneous Nonlinearities
3 Multiple Hopf Bifurcations
3.1 The Zeros of Successor Functions in the Polar Coordinates
3.2 Analytic Equivalence
3.3 Quasi Successor Function
3.4 Bifurcations of Limit Circle of a Class of Quadratic Systems
4 Isochronous Center In Complex Domain
4.1 Isochronous Centers and Period Constants
4.2 Linear Recursive Formulas to Compute Period Constants
4.3 Isochronous Center for a Class of Quintic System in the Complex Domain
4.3.1 The Conditions of Isochronous Center Under Condition C1
4.3.2 The Conditions of Isochronous Center Under Condition C2
4.3.3 The Conditions of Isochronous Center Under Condition C3
4.3.4 Non-Isochronous Center under Condition C4 and C* 4
4.4 The Method of Time-Angle Difference
4.5 The Conditions of Isochronous Center of the Origin for a Cubic System
5 Theory of Center-Focus and Bifurcation of Limit Cycles at Infinity of a Class of Systems
5.1 Definition of the Focal Values of Infinity
5.2 Conversion of Questions
5.3 Method of Formal Series and Singular Point Value of Infinity
5.4 The Algebraic Construction of Singular Point Values of Infinity
5.5 Singular Point Values at Infinity