Korteweg-de vries and nonlinear Schröginger [i.e. Schrödinger] equations : qualitative theory
著者
書誌事項
Korteweg-de vries and nonlinear Schröginger [i.e. Schrödinger] equations : qualitative theory
(Lecture notes in mathematics, 1756)
Springer-Verlag, c2001
大学図書館所蔵 全74件
  青森
  岩手
  宮城
  秋田
  山形
  福島
  茨城
  栃木
  群馬
  埼玉
  千葉
  東京
  神奈川
  新潟
  富山
  石川
  福井
  山梨
  長野
  岐阜
  静岡
  愛知
  三重
  滋賀
  京都
  大阪
  兵庫
  奈良
  和歌山
  鳥取
  島根
  岡山
  広島
  山口
  徳島
  香川
  愛媛
  高知
  福岡
  佐賀
  長崎
  熊本
  大分
  宮崎
  鹿児島
  沖縄
  韓国
  中国
  タイ
  イギリス
  ドイツ
  スイス
  フランス
  ベルギー
  オランダ
  スウェーデン
  ノルウェー
  アメリカ
注記
Includes bibliographical references (p. [137]-146) and index
内容説明・目次
内容説明
- of nonlinear the of solitons the the last 30 theory partial theory During years - has into solutions of a kind a differential special equations (PDEs) possessing grown and in view the attention of both mathematicians field that attracts physicists large and of the of the problems of its novelty problems. Physical important applications for in the under consideration are mo- to the observed, example, equations leading mathematical discoveries is the Makhankov One of the related V.G. by [60]. graph from this field methods that of certain nonlinear by equations possibility studying inverse these to the problem; equations were analyze quantum scattering developed this method of the inverse called solvable the scattering problem (on subject, are by known nonlinear At the the class of for same time, currently example [89,94]). see, the other there is solvable this method is narrow on hand, PDEs sufficiently and, by of differential The latter called the another qualitative theory equations. approach, the of various in includes on pr- investigations well-posedness approach particular solutions such or lems for these the behavior of as stability blowing-up, equations, these and this of approach dynamical systems generated by equations, etc., properties in wider class of a makes it to an problems (maybe possible investigate essentially more general study).
目次
Introduction Notation Chapter 1. Evolutionary equations. Results on existance 1.1 The (generalized Korteweg-de Vries equation (KdVE) 1.2 The nonlinear Schroedinger equation (NLSE) 1.3 On the blowing up of solutions 1.4 Additional remarks Chapter 2. Stationary problems 2.1 Existence of solutions. An ODE approach 2.2 Existence of solutions. A variational method 2.3 The concentration-compactness method of P.L. Lions 2.4 On basis properties of systems of solutions 2.5 Additional remarks Chapter 3. Stability of solutions 3.1 Stability of soliton-like solutions 3.2 Stability of kinks for the KdVE 3.3 Stability of solutions of the NLSE non-vanishing as (x) to infinity 3.4 Additional remarks Chapter 4. Invariant measures 4.1 On Gaussian measures in Hilbert spaces 4.2 An invariant measure for the NLSE 4.3 An infinite series of invariant measures for the KdVE 4.4 Additional remarks Bibliography Index
「Nielsen BookData」 より