Guo Y., Biswas A. Nonlinear Evolution Equations and Soliton Solutions

New York, USA: Nova Science Publishers, Inc., 2016. — 487 p. — (Mathematics Research Developments). — ISBN: 1634827694.Soliton attracts much attention in academia and industry because of its beautiful structure and a wide range of applications. During half a century period of its rapid development, there have been many monographs and related books published. Among them there are a few to clarify the mechanism of formation and propagation of solitons. Professor Guo's book focuses on them through utilizing her recent year publications. In the book, Professor Guo describes several mathematical models in detail to generate soliton solutions. Those mathematical models are usually called nonlinear evolution equations, including the KdV equation, the nonlinear Schrodinger equation, the Sine-Gordon equation, and so on. The principal of formation of solitons is actually caused due to precise balance between dispersion phenomena and nonlinear effect in fluctuations is described clearly in the book.
This book will provide some tools for solving nonlinear partial differential equations to get solitary wave solutions in an explicit formula. Those tools include the Inverse Scattering Transformation method, Backlund Transformation method, Similarity Transformation methods, and other Special Transformation methods, which are all classic and practical. Basically, they play a fundamental and powerful role in getting soliton solutions for an integrable system.
The book provides the principles and applications for those methods with detailed procedure and accurate computations. The book also covers the integrability and Painleve property of nonlinear partial differential equations, and describes the amazing application prospect of solitons - optical soliton communication. So this book is one of very good sources for graduate students and fresh researchers to grasp some procedure to solve nonlinear partial differential equations with solitary wave/soliton solutions as well as suitable for a graduate class as a textbook or a reference. This book is also one of good reference choice for researchers engaged in the field of nonlinear science.Typical Equations and their Solitary Wave Solutions
The Inverse Scattering Method and Multiple Solitary Wave Solutions
Bäcklund Transformation
Integrability and Painlevè Property of Nonlinear Differential Equations
Similarity Transformation and Similar Solutions of Nonlinear Partial Differential Equations
Special Transformation Methods for Solving Nonlinear Partial Differential Equations
Optical Solitons
Appendixes
Elliptic Functions and Elliptic Equations
The First Integral and the Solution Methods of First-Order Partial Differential Equations
Some Concepts and Terminologies Associated with Fluctuations
Introduction of Perturbation Method
Hypergometric Function and Hypergometric Series