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Solitons /
A 'soliton' is a localized nonlinear wave of permanent form which may interact strongly with other solitons so that when they separate after the interaction they regain their original forms. This textbook is an account of the theory of solitons and of the diverse applications of the theory...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York :
Cambridge University Press,
1983.
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| Colección: | London Mathematical Society lecture note series ;
85. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title; Copyright; Contents; Preface; Chapter 1 TEE KORTEWEG-DE VRIES EQUATION; 1. The discovery of solitary waves; 2. Fundamental ideas; 3. The discovery of soliton interactions; 4. Applications of the KdV equation; Problems; CHAPTER 2 CNOIDAL WAVES; 1. Wave solutions of the KdV solution; 2. Solitary waves; 3. General waves of permanent form; 4. Description of waves in terms of elliptic functions; 5. Infinitesimal waves; 6. Solitary waves again; Problems; Chapter 3 CONSERVATION LAWS; 1. Fundamental ideas; 2. Gardner's transformation; Problems
- Chapter 4 THE INITIAL-VALUE PROBLEM FOR THE KORTEWEG-DE VRIES EQUATION1. The problem; 2. Sketch of the method of inverse scattering; 3. The scattering problem; 4. The evolution equation; 5. Solution of the scattering problem for t> 0; 6. The inverse scattering problem; 7. Qualitative character of the solution; 8. Example: the delta-function potential; 9. Example: g(x) =
- 2sech2x; 10. Example: g(x) =
- 6sech2x; 11. Examples: sech-squared potentials; 12. Examples: some numerical results; 13. Reflectionless potentials; Chapter 5 THE LAX METHOD
- 1. Description of the method in terms of operatorsProblems; Chapter 6 THE SINE-GORDON EQUATION; 1. Introduction; 2. Waves and solitons; 3. Some other simple explicit solutions; 4. The interaction of two solitons; 5. A breather; 6. The method of inverse scattering; Problems; Chapter 7 BACKLUND TRANSFORMATIONS; 1. Introduction; 2. The sine-Gordon equation; 3. The KdV equation; Problems; 1. Epilogue; Appendix A DERIVATION OF THE INTEGRAL EQUATION FOR INVERSE SCATTERING; Bibliography and author index; Motion picture index; Subject index