Nonlinear evolution equations and soliton solutions /
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 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
9781634841580 1634841581 (hardcover)
2015050010
Evolution equations, Nonlinear.
Solitons.
Transformations (Mathematics)
Differential equations, Nonlinear.
Équations d'évolution non linéaires.
Solitons.
Équations différentielles non linéaires.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Differential equations, Nonlinear.
Evolution equations, Nonlinear.
Solitons.
Transformations (Mathematics)
Electronic books.
QC20.7.E88
515/.353
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 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
9781634841580 1634841581 (hardcover)
2015050010
Evolution equations, Nonlinear.
Solitons.
Transformations (Mathematics)
Differential equations, Nonlinear.
Équations d'évolution non linéaires.
Solitons.
Équations différentielles non linéaires.
MATHEMATICS--Calculus.
MATHEMATICS--Mathematical Analysis.
Differential equations, Nonlinear.
Evolution equations, Nonlinear.
Solitons.
Transformations (Mathematics)
Electronic books.
QC20.7.E88
515/.353