Solitons in Multidimensions: Inverse Spectral Transform Method
- ISBN-10
- 9814518069
- ISBN-13
- 9789814518062
- Pages
- 304
- Language
- English
- Published
- 1993-04-30
- Publisher
- World Scientific
- Author
- B G Konopelchenko
Description
The book is devoted to the mathematical theory of soliton phenomena on the plane. The inverse spectral transform method which is a main tool for the study of the (2+1)-dimensional soliton equation is reviewed. The ∂-problem and the Riemann-Hilbert problem method are discussed. Several basic examples of soliton equations are considered in detail. This volume is addressed both to the nonexpert and to the researcher in the field. This is the first literature dealing specifically with multidimensional solition equations. Contents:IntroductionDressing Method, The Kadomtsev-Petviashvili EquationThe Modified Kadomtsev-Petviashvili EquationThe Davey-Stewartson EquationThe Ishimori EquationThe 2+1-Dimensional Integrable Sine-Gordon EquationExtensions of the ∂-Dressing Method Readership: Applied mathematicians, mathematical physicists and researchers in chaos and in nonlinear sciences. keywords:Bibliography;Korteweg De Vries Equation;Dressing Method;Riemann-Hilbert Problems;Inverse Scattering Transform;Kadomtsev-Petviashvili Equations;Modified Kadomtsev-Petviashvili Equations;Modified Korteweg- De Vries Equation;Miura Transform;Davey-Stewartson Equations;Ishimori Equations;Heisenberg-Ferromagnet Model;Sine-Gordon Equation “The remarkable discovery for the algebraic structure governing the sequence of conserved quantities in the kdV, KP or non-linear Schrödinger dynamics was a long time restricted to a one-dimensional spatial coordinate system. The multidimensional analogs are much harder and for this reason very intriguing to tame. The book by Konopelchenko offers a first organized exposition of the inverse spectral transform technique applied to 2D integrable systems of the same category. The elegant and original combination of complex analysis, spectral theory and infinite dimensional algebra is a high mark of this text.” Professor Mihai Putinar University of California at Santa Barbara
