Bäcklund transformations and their applications / C. Rogers and W.F. Shadwick.

Includes bibliographical references (pages 302-321) and indexes.

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Ba?cklund transformations and their applications.

Front Cover; Bäcklund Transformations and Their Applications; Copyright Page; Contents; Preface; Acknowledgments; General Introduction and Outline; CHAPTER 1. Bäcklund Transformations and Their Application to Nonlinear Equations of Mathematical Physics; 1.1 The Origin and Importance of Bäcklund 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 Bäcklund 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-Bäcklund Transformation of the Modified Korteweg-deVries Equation. The Permutability Theorem and Generation of Solutions

1.9 The Miura Transformation1.10 A Nonlinear Schrödinger Equation; 1.11 Bäcklund Transformations and the AKNS System. An Invariant Transformation of the Cubic Schrödinger Equation; 1.12 The Hirota Bilinear Operator Formulation of Bäcklund Transformations. The Boussinesq Equation. Kaup's Higher Order Water Wave Equation; 1.13 Bäcklund Transformations for Higher Order Korteweg-deVries Equations; 1.14 Bäcklund 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 Bäcklund Transformation for Joseph's Equation for Internal Waves in a Stratified Fluid with Finite Depth; 1.17 Bäcklund Transformations of Nonlinear Lattice Equations in Their Continuum Approximation. The Konno-Sanuki Transformation; 1.18 Bäcklund Transformations of Nonlinear Differential-Difference Equations. The Toda and Associated Lattices; 1.19 Bäcklund Transformations in General Relativity. The Ernst Equations. Neugebauer's Permutability Theorem

CHAPTER 2. A Local Jet-Bundle Formulation of Bäcklund Transformations2.1 Preliminaries; 2.2 Contact Structures; 2.3 Partial Differential Equations on Jet Bundles; 2.4 Fibered Products of Jet Bundles; 2.5 Bäcklund Maps; 2.6 Bäcklund Transformations Determined by Bäcklund Maps; 2.7 Symmetries of Differential Equations and One-Parameter Families of Bäcklund Maps; 2.8 The Wahlquist-Estabrook Procedure; CHAPTER 3. Bäcklund Transformations in Gasdynamics, Nonlinear Heat Conduction, and Magnetogasdynamics; 3.1 The Reciprocal Relations and the Haar Transformation

English.

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