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The inverse scattering transformation and the theory of solitons : an introduction /
The Inverse Scattering Transformation and The Theory of Solitons.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York : New York :
North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier North-Holland,
�1981.
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| Colección: | North-Holland mathematics studies ;
50. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; The Inverse Scattering Transformation and The Theory of Solitons; Copyright Page; TABLE OF CONTENTS; PREFACE; CHAPTER 1. THE KORTEWEG-DE VRIES EQUATION; 1.1. Historical introduction; 1.2. Elementary properties; 1.3. The soliton behaviour; 1.4. The initial value problem, Existence and uniqueness of solutions; 1.5. Miura's transformation and the modified; CHAPTER 2. SOLUTION BY THE METHOD OF GARDNER-GREEN-KRUSKAL- MIURA. THE INVERSE SCATTERING TRANSFORMATION; 2.1. The scattering problem for the Sch�Odinger equation on the line
- 2.2. Invariance of the spectrum for potentials satisfying the K.D.V. equation2.3. Evolution of the scattering data; 2.4. Summary and discussion of the method of solution by the inverse scattering transformation; 2.5. The pure N-soliton solution; 2.6. The pure 2-soliton solution: an exercise; 2.7. Relation between soliton speed and eigenvalues; 2.8. The emergence of solitons from arbitrary initial conditions; CHAPTER 3. ISOSPECTRAL POTENTIALS. THE LAX APPROACH; 3.1. The invariance of discrete eigenvalues by an elementary approach; 3.2. The invariance of the spectrum
- 3.3. Isospectral potentials for the Schr�Odinger equation3.4. Isospectral potentials for more general selfadjoint operators; 3.5. An alternative approach; CHAPTER 4. DIRECT AND INVERSE SCATTERING FOR THE SCHR�ODINGER'S EQUATION; 4.1. Solutions and scattering data of Schr�odinger's equation; 4.2. Properties of solutions; 4.3. The spectrum of
- d2/DX2 + u on L2(m); 4.4. Fourier transform of the solutions; 4.5. Inverse scattering; 4.6. Concluding remarks; CHAPTER 5. DIRECT AND INVERSE SCATTERING FOR THE GENERATED ZAKHAROV-SHABAT SYSTEM
- 5.1. Solutions and scattering coefficients of the generalized Zakharov-Shabat system5.2. Properties of solutions; 5.3. The spectrum of (100-1)(d/dx=Q) ON L2(IR)2; 5.4. Fourier transform of solutions; 5.5. Inverse scattering; CHAPTER 6. APPLICATIONS OF THE INVERSE SCATTERING; 6.1. The nonlinear Schr�Odinger equation; 6.2. Isospectral potentials for nondegenerate first order system using an alternative approach; 6.3. Some evolution equations for isospectral potentials by ad hoc prosedures; 6.4. The general AKNS evolution equations
- 6.5. Degenerate first order scattering systems and the sine-Gordon equation6.6. Higher order scattering systems; CHAPTER 7. PERTURBATIONS; 7.1. Introduction and general formulation; 7.2. Evolution of the Scattering data in the case of the Schr�odinger equation; 7.3. Evolution of the scattering data in the case of the generalized Zakharov-Shabat problem; 7.4. Perturbation analysis; REFERENCES