This book provides an up-to-date overview of mathematical theories and research results on solitons, presenting related mathematical methods and applications as well as numerical experiments. Different types of soliton equations are covered along with their dynamical behaviors and applications from physics, making the book an essential reference for researchers and graduate students in applied mathematics and physics.

Contents
Introduction

Inverse scattering transform

Asymptotic behavior to initial value problems for some integrable evolution nonlinear equations

Interaction of solitons and its asymptotic properties

Hirota method

Bäcklund transformations and the infinitely many conservation laws

Multi-dimensional solitons and their stability

Numerical computation methods for some nonlinear evolution equations

The geometric theory of solitons

Global existence and blow up for the nonlinear evolution equations

The soliton movements of elementary particles in nonlinear quantum field

The theory of soliton movement of superconductive features

The soliton movements in condensed state systemsontents