Nonlinear evolution equations and soliton solutions /
Saved in:
| Other Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Hauppauge, New York :
Nova Science Publishers, Inc.,
2016.
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| Series: | Mathematics research developments
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| Subjects: | |
| Online Access: | CONNECT |
Table of Contents:
- NONLINEAR EVOLUTION EQUATIONS AND SOLITON SOLUTIONS ; NONLINEAR EVOLUTION EQUATIONS AND SOLITON SOLUTIONS ; Library of Congress Cataloging-in-Publication Data; CONTENTS; FOREWORD ; PREFACE; Chapter 1 TYPICAL EQUATIONS AND THEIR SOLITARY WAVE SOLUTIONS ; 1.1. THE HISTORICAL REVIEW; 1.2. SOLITARY WAVE
- THE BALANCE BETWEEN NONLINEAR CONVERGENCE AND DISPERSION PHENOMENON ; 1.2.1. Nonlinear Convergence Phenomenon in Fluctuations ; 1.2.2. The Dispersion in Fluctuations ; 1.2.3. The Balance of Convergence Effect and Dispersion Effect
- The Explanation of KdV Equation
- 1.3. KDV EQUATION AND ITS SOLITARY WAVE SOLUTION 1.3.1. Derivation of KdV Equation ; 1.3.2. The Solitary Wave Solution of KdV Equation ; 1.3.3. Generalized KdV Equations and Their Solitary Wave Solutions ; 1.3.3.1. The Solitary Wave Solution of mKdV Equation ; 1.3.3.2. Solitary Wave Solution of Boussinesq Equation ; 1.3.3.3. Solitary Wave Solution of KP (Kadomtsev-Petviashvili) Equation ; 1.4. NONLINEAR SCHRÖDINGER EQUATION AND OPTICAL SOLITON ; 1.4.1. Derivation of the Nonlinear Schrödinger Equation ; 1.4.2. The Single Solitary Wave Solution of Nonlinear Schrödinger Equation
- 1.4.3. The Solitary Wave Solution Having Traveling Wave Form of Nonlinear Schrödinger Equation 1.5. THE NONLINEAR SINE-GORDON EQUATION; 1.5.1. The Josephson Effect and Nonlinear Sine-Gordon Equation ; 1.5.2. The Solitary Wave Solution of Nonlinear Sine-Gordon Equation ; 1.5.3. The Breather-Typed Soliton Solution of Nonlinear Sine-Gordon Equation ; 1.6. BURGERS EQUATION AND ITS SOLITARY WAVE SOLUTION ; 1.6.1. The Derivation of the Burgers Equation as a Transport Model ; 1.6.2. Solitary Wave Solutions of Burgers Equation ; 1.6.3. The Hopf-Cole Transformation
- Chapter 2 THE INVERSE SCATTERING METHOD AND MULTIPLE SOLITARY WAVE SOLUTIONS 2.1. THE SCATTERING AND INVERSE SCATTERING PROBLEMS ; 2.1.1. The Single Soliton Solution ; 2.1.2. The Double Soliton Solution ; 2.2. THE EVOLUTION OF THE SCATTERING DATA OVER TIME ; 2.3. THE SPECIFIC PROCESS OF SOLVING KDV EQUATION USING INVERSE SCATTERING METHOD AND THE PROOF OF INVERSION THEOREM ; 2.4. THE N SOLITON SOLUTION OF KDV EQUATION ; 2.4.1. The Single Soliton Solution of KdV Equation ; 2.4.2. The Double-Soliton Solution of KdV Equation ; 2.4.3. The N Soliton Solution of KdV Equation
- 2.5. THE PROMOTION OF INVERSE SCATTERING METHOD2.5.1. Lax Equation ; 2.5.2. AKNS Method ; 2.6. THE INVERSE SCATTERING METHOD FOR SOLVING NONLINEAR SCHRÖDINGER EQUATION ; 2.6.1. The Basic Idea ; 2.6.2. The Determination of Lax Pair of Nonlinear Schrödinger Equation ; 2.6.3. The Direct Scattering Problem-Intrinsic Value Problem ; 2.6.3.1. The Solution of Two-Component system and the Characteristics of Scattering Data ; 2.6.3.2. The Solution of Two-Component System and the Determination of Scattering Data ; 2.6.4. The Evolution of the Scattering Data Over Time
