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B�acklund transformations and their applications /
Ba?cklund transformations and their applications.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
New York :
Academic Press,
1982.
|
| Colección: | Mathematics in science and engineering ;
v. 161. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo Texto completo |
Tabla de Contenidos:
- Front Cover; B�acklund Transformations and Their Applications; Copyright Page; Contents; Preface; Acknowledgments; General Introduction and Outline; CHAPTER 1. B�acklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics; 1.1 The Origin and Importance of B�acklund Transformations; 1.2 The 1 + 1 Sine-Gordon Equation. The Permutability Theorem. Bianchi Diagrams; 1.3 Ultrashort Optical Pulse Propagation in a Resonant Medium. 2Np Light Pulses
- 1.4 Propagation of Magnetic Flux through a Long Josephson Junction. An Elliptic Analog of the 1 + 1 Sine-Gordon Equation. Generation of Solutions via a B�acklund Transformation1.5 The Cole-Hopf Reduction of Burgers' Equation to the Heat Equation. Solution of Initial Value Problems; 1.6 Finite Amplitude Dispersive Waves and the Korteweg-deVries Equation; 1.7 The Wahlquist-Estabrook Invariant Transformation of the Korteweg-deVries Equation. The Soliton Ladder; 1.8 An Auto-B�acklund Transformation of the Modified Korteweg-deVries Equation. The Permutability Theorem and Generation of Solutions
- 1.9 The Miura Transformation1.10 A Nonlinear Schr�odinger Equation; 1.11 B�acklund Transformations and the AKNS System. An Invariant Transformation of the Cubic Schr�odinger Equation; 1.12 The Hirota Bilinear Operator Formulation of B�acklund Transformations. The Boussinesq Equation. Kaup's Higher Order Water Wave Equation; 1.13 B�acklund Transformations for Higher Order Korteweg-deVries Equations; 1.14 B�acklund Transformations in Higher Dimensions. The Sine-Gordon Equation in 3 + 1 Dimensions. The Kadomtsev-Petviashvili Equation. The Yang Equations
- 1.15 The Benjamin-Ono Equation for Internal Deep Water Waves. The Nakamura Transformation1.16 A B�acklund Transformation for Joseph's Equation for Internal Waves in a Stratified Fluid with Finite Depth; 1.17 B�acklund Transformations of Nonlinear Lattice Equations in Their Continuum Approximation. The Konno-Sanuki Transformation; 1.18 B�acklund Transformations of Nonlinear Differential-Difference Equations. The Toda and Associated Lattices; 1.19 B�acklund Transformations in General Relativity. The Ernst Equations. Neugebauer's Permutability Theorem
- CHAPTER 2. A Local Jet-Bundle Formulation of B�acklund Transformations2.1 Preliminaries; 2.2 Contact Structures; 2.3 Partial Differential Equations on Jet Bundles; 2.4 Fibered Products of Jet Bundles; 2.5 B�acklund Maps; 2.6 B�acklund Transformations Determined by B�acklund Maps; 2.7 Symmetries of Differential Equations and One-Parameter Families of B�acklund Maps; 2.8 The Wahlquist-Estabrook Procedure; CHAPTER 3. B�acklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics; 3.1 The Reciprocal Relations and the Haar Transformation