Spectral methods in soliton equations
著者
書誌事項
Spectral methods in soliton equations
（Pitman monographs and surveys in pure and applied mathematics, 73）
Longman Scientific & Technical , Wiley, 1994
大学図書館所蔵 件 / 全40件
-
該当する所蔵館はありません
- すべての絞り込み条件を解除する
注記
Includes bibliographical references (p. [369]-384)
内容説明・目次
内容説明
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.
目次
Introduction
Spectral theory of the regular A-operators
Spectral theory for A-operators on the semi-axis
A-operators on the line and nonlinear evolution equations
Stability of solitary wave solutions for nonlinear evolution equations
Bibliography
「Nielsen BookData」 より