Bilinear transformation method, Volume 174 (Mathematics in Science and Engineering)

✍ Scribed by Matsuno (editor)

• Publisher: Academic Press
• Year: 1984
• Tongue: English
• Leaves: 233
• Category: Library

✦ Table of Contents

Front Cover
Bilinear Transformation Method
Copyright Page
Contents
Preface
Chapter 1. Introduction and Outline
1.1 Introduction
1.2 Outline
Chapter 2. Introduction to the Bilinear Transformation Method
2.1 Bilinearization
2.2 Exact Solutions
2.3 Bäcklund Transformation
2.4 Conservation Laws
2.5 Inverse Scattering Method
2.6 Bibliography
Chapter 3. The Benjamin–Ono Equation
3.1 Multisoliton Solutions of the Benjamin–Ono Equation
3.2 Bäcklund Transformation and Conservation Laws of the Benjamin–Ono Equation
3.3 Asymptotic Solutions of the Benjamin–Ono Equation
3.4 Stability of the Benjamin–Ono Solitons
3.5 The Linearized Benjamin–Ono Equation and Its Solution
Chapter 4. Interaction of the Benjamin–Ono Solitons
4.1 Asymptotic Behaviors of the N-Soliton Solution
4.2 Interaction of Two Solitons
Chapter 5. The Benjamin–Ono-Related Equations
5.1 Higher-Order Benjamin–Ono Equations
5.2 Higher-Order Korteweg–de Vries Equations
5.3 The Finite-Depth Fluid Equation and Its Higher-Order Equations
5.4 Higher-Order Modified Korteweg–de Vries Equations
5.5 Bäcklund Transformations and Inverse Scattering Transforms of Higher-Order Korteweg–de Vries Equations
Chapter 6. Topics Related to the Benjamin–Ono Equation
6.1 The Modified Benjamin–Ono Equation
6.2 The Derivative Nonlinear Schrödinger Equation
6.3 The Perturbed Benjamin–Ono Equation
Appendix I: Formulas of the Bilinear Operators
Appendix II: Properties of the Matrices M and A
Appendix III: Properties of the Hilbert Transform Operator
Appendix IV: Proof of (3.274)
References
Author Index
Subject Index