Nonlinear evolution equations and soliton solutions /
editors, Yucui Guo, and Anjan Biswas (Beijing University of Post and Telecommunications, Beijing, China, and others).
- 1 online resource
- Mathematics research developments .
Includes index.
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 SCHR�ODINGER EQUATION AND OPTICAL SOLITON ; 1.4.1. Derivation of the Nonlinear Schr�odinger Equation ; 1.4.2. The Single Solitary Wave Solution of Nonlinear Schr�odinger Equation 1.4.3. The Solitary Wave Solution Having Traveling Wave Form of Nonlinear Schr�odinger 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 SCHR�ODINGER EQUATION ; 2.6.1. The Basic Idea ; 2.6.2. The Determination of Lax Pair of Nonlinear Schr�odinger 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