Title Statements
- Full title :Semi-classical Analysis For Nonlinear Schrodinger Equations
Edition Statements
- Publication Date:2020.
Publication Statements
- Publisher(s):World scientific Publishing Company
- Place of Publication:Singapore
- Language:eng
- Publication Date:2020.
Notes
Description based upon print version of record.
The Physical Object
- Description:1 online resource (367 p.)
Edition Identifiers
- ISBN:9789811227912, 9811227918
- oclc:on1204135484
Table of Contents
Intro -- Contents -- Preface -- WKB Analysis -- 1. Preliminary Analysis -- 1.1 General presentation -- 1.2 Formal derivation of the equations -- 1.3 Linear Schrödinger equation -- 1.3.1 The eikonal equation -- 1.3.2 The transport equations -- 1.4 Basic results in the nonlinear case -- 1.4.1 Formal properties -- 1.4.2 Strong solutions -- 1.4.3 Mild solutions -- 1.4.4 Weak solutions -- 2. Weakly Nonlinear Geometric Optics -- 2.1 Improved existence results -- 2.2 Leading order asymptotic analysis -- 2.3 Interpretation -- 2.4 Higher order asymptotic analysis
2.5 An application: Cauchy problem in Sobolev spaces for nonlinear Schrödinger equations with potential -- 2.6 Multiphase expansions -- 2.6.1 Resonant phases -- 2.6.2 The set of transport equations -- 2.6.3 Functional setting -- 2.6.4 Error estimate -- 3. Convergence of Quadratic Observables via Modulated Energy Functionals -- 3.1 Presentation -- 3.2 Formal computation -- 3.3 Justification -- 3.3.1 The Cauchy problem for (3.3) -- 3.3.2 Rigorous estimates for the modulated energy -- 3.4 Convergence of quadratic observables -- 4. Pointwise Description of the Wave Function
6.1 Presentation -- 6.2 The idea of J. Hunter and J. Keller…
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