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Singularities of solutions to nonlinear Schrödinger equations

Fumihito Abe, Keiichi Kato

Abstract

We study the wave front set of the solutions of the initial value problem for nonlinear Schrödinger equations via wave packet transform. We give an sufficient condition which assures that the solutions is in Sobolev space of order s in a given direction at a given time.

Singularities of solutions to nonlinear Schrödinger equations

Abstract

We study the wave front set of the solutions of the initial value problem for nonlinear Schrödinger equations via wave packet transform. We give an sufficient condition which assures that the solutions is in Sobolev space of order s in a given direction at a given time.

Paper Structure

This paper contains 5 sections, 55 equations.

Table of Contents

  1. Introduction
  2. Wave packet transform and characterization of wave front set
  3. Transformed equations
  4. Proof of Theorem \ref{['2']}
  5. Proof of Lemma \ref{['4.1']}

Theorems & Definitions (4)

  • proof : (Proof of Remark \ref{['rem']})
  • proof : (Proof of Theorem \ref{['2']})
  • proof
  • proof