Algebraic and spectral methods for nonlinear wave equations
Author(s)
Bibliographic Information
Algebraic and spectral methods for nonlinear wave equations
（Pitman monographs and surveys in pure and applied mathematics, v. 49）
Longman Scientific & Technical , Wiley, 1990
Available at / 35 libraries
-
Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science図書
dc19:530/as132070184504
-
No Libraries matched.
- Remove all filters.
Description and Table of Contents
Description
This volume outlines the basic features of algebraic and spectral methods for nonlinear wave equations, or systems of partial differential equations frequently used in science and engineering. The book covers fundamental materials of the Lie's transformation method, inverse scattering formulation and developments in these and related fields, marked by the discovery of soliton by Zabusky and Kruskal in 1967. The subjects covered are Lie-Backlund symmetries (generalized symmetries), Backlund transformation, recursion operator for the symmetries, Lax representation, variational formalism, analysis of the inverse scattering method, bilinear form method, Riemann-Hilbert problem and the periodic boundary value problem of the inverse scattering method. In the course of the presentation, this volume also introduces the Wahlquist-Estabrook method, Hamiltonian formalism, dressing method by Zakharov-Shabat and a-problem. Some of the topics covered are presented in book form for the first time. The book is intended for students and specialists in mathematical physics, applied mathematics and related fields.
Readers are not required to have the knowledge of more than university mathematics for engineering and physics.
Table of Contents
- Part 1 Point transformation: local coordinate transformation
- prolongation of the point transformation
- analysis of the PDEs and their solutions. Part 2 Higher order transformation: point transformation on J to the K (M,N)
- Lie-Backlund transformation 1
- examples and applications of BT. Part 3 Recursion operator and lax pair: recursion operator and lax representation - recursion operator for symmetry, examples of the recursion operators, symmetry algebra for the isentropic flow equation
- construction of recursion operator - algebras
- conditions for the existence, construction of the operators
- recursion operator for matrix evolution equations - evolution equations, hereditary property of L
- Wahlguist Estabrook method - differential forms, WE prolongation method
- Backlund transformation II - BT via recursion operator, BT via gauge transformation. Part 4 Variational formalism: variational calculus - Eular-Lagrange equation, image of Eular operator
- conservation laws and symmetries - conservation law
- conservation laws and symmetries
- Hamiltonian formalism - poisson bracket, determination of H, symmetry and conservation law. Part 5 Inverse scattering method: lax theory and the Zakharov-Shabat-Ablowitz-Kaup-Newell-Segur system - solitons and the lax theory, Zakharov-Shabat-Ablowitz-Kaup-Newll-Segur system
- jost solutions and the scattering matrix - Zakharov-Shabat equation, integral equations for the Zakharov-Shabat equation, classes of matrix functions, Jost solutions, scattering matrix of the Jost solutions
- inverse scattering problem - Marchenko equation, inverse scattering transform, scattering data, kernel of the Marchenko equation, solution of the Marchenko equation
- inverse scattering method - evolution of the scattering data, algorism of the inverse scattering method, burst of the solution, solitions. Part 6 Inverse scattering and related methods: solutions of the Korteweg-de Vries equation
- Jost solutions, Wronskians of the Jost solutions, Zeros of the Wronskian, Marchenko equation, solution of the Marchenko equation, evolution of the scattering data, solutions of the KdV equation. (Part Contents)
by "Nielsen BookData"