Long range scattering for the nonlinear Schrödinger equation with higher order anisotropic dispersion in two dimensions

Jean Claude Saut, Jun ichi Segata

Research output: Contribution to journalArticle

Abstract

This paper is a continuation of our previous study [13] on the long time behavior of solution to the nonlinear Schrödinger equation with higher order anisotropic dispersion (4NLS). We prove the long range scattering for (4NLS) with the quadratic nonlinearity in two dimensions. More precisely, for a given asymptotic profile u+, we construct a solution to (4NLS) which converges to u+ as t→∞, where u+ is given by the leading term of the solution to the linearized equation of (4NLS) with a logarithmic phase correction.

Original languageEnglish
Article number123638
JournalJournal of Mathematical Analysis and Applications
Volume483
Issue number2
DOIs
Publication statusPublished - Mar 15 2020

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Asymptotic Profile
Scattering Problems
Long-time Behavior
Behavior of Solutions
Nonlinear equations
Nonlinear Schrödinger Equation
Continuation
Two Dimensions
Logarithmic
Scattering
Nonlinearity
Higher Order
Converge
Term
Range of data

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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