## Table of Contents

**Table of Contents**

Foreword

(Dr. Zhijun Qiao)

pp. vii-viii

Preface

pp. ix-xiii

Chapter 1

Typical Equations and their Solitary Wave Solutions

pp. 1-70

Chapter 2

The Inverse Scattering Method and Multiple Solitary Wave Solutions

pp. 71-158

Chapter 3

Bäcklund Transformation

pp. 159-190

Chapter 4

Integrability and Painlevè Property of Nonlinear

Differential Equations

pp. 191-218

Chapter 5

Similarity Transformation and Similar Solutions of Nonlinear

Partial Differential Equations

pp. 219-280

Chapter 6

Special Transformation Methods for Solving Nonlinear Partial

Differential Equations

pp. 281-352

Chapter 7

Optical Solitons

pp. 353-400

Appendix A

Elliptic Functions and Elliptic Equations

pp. 401-410

Appendix B

The First Integral and the Solution Methods of First-Order

Partial Differential Equations

pp. 411-434

Appendix C

Some Concepts and Terminologies Associated with Fluctuations

pp. 435-452

Appendix D

Introduction of Perturbation Method

pp. 453-454

Appendix E

Hypergometric Function and Hypergometric Series

pp. 455-458

References

pp. 459-466

Author Contact Information

pp. 467

Index

pp. 469-472

This book is written for graduate students and teachers whose fields are applied mathematics, applied physics, nonlinear science, and other relative areas. It can be used as textbook and reference book, and it is also available for researchers engaged in research on nonlinear science and theory of solitons as a reference book.