Spectral Methods in Soliton Equations

1. Auflage 1994
ISBN: 978-0-582-23963-0
Verlag: Chapman and Hall/CRC

Buch, Englisch, Band 73, 400 Seiten, Format (B × H): 216 mm x 279 mm, Gewicht: 725 g

Reihe: Monographs and Surveys in Pure and Applied Mathematics

Soliton theory as a method for solving some classes of nonlinear evolution equations (soliton equations) is one of the most actively developing topics in mathematical physics. This book presents some spectral theory methods for the investigation of soliton equations ad the inverse scattering problems related to these equations. The authors give the theory of expansions for the Sturm-Liouville operator and the Dirac operator. On this basis, the spectral theory of recursion operators generating Korteweg-de Vries type equations is presented and the Ablowitz-Kaup-Newell-Segur scheme, through which the inverse scattering method could be understood as a Fourier-type transformation, is considered. Following these ideas, the authors investigate some of the questions related to inverse spectral problems, i.e. uniqueness theorems, construction of explicit solutions and approximative methods for solving inverse scattering problems. A rigorous investigation of the stability of soliton solutions including solitary waves for equations which do not allow integration within inverse scattering method is also presented.

Autoren/Hrsg.

Iliev, I. D.

Khristov, Eugeni

Kirchev, Kiril Petrov

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

IntroductionSpectral theory of the regular A-operatorsSpectral theory for A-operators on the semi-axisA-operators on the line and nonlinear evolution equationsStability of solitary wave solutions for nonlinear evolution equationsBibliography