Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrödinger type equation

Junichi Segata, Akihiro Shimomura

Research output: Contribution to journalArticle

Abstract

We study the global existence and asymptotic behavior in time of solutions to the fourth order nonlinear Schrödinger type equation in one space dimension. The nonlinear interaction is the power type interaction with degree three, and it is a summation of a gauge invariant term and non-gauge-invariant terms. We prove the existence of modified wave operators for this equation with small final states. Here the modification of wave operator is only derived from the gauge invariant nonlinearity.

Original languageEnglish
Pages (from-to)169-188
Number of pages20
JournalCommunications in Applied Analysis
Volume11
Issue number2
Publication statusPublished - Apr 1 2007
Externally publishedYes

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Asymptotic Behavior of Solutions
Global Existence
Gages
Fourth Order
Wave Operator
Invariant
Gauge
Nonlinear Interaction
Term
Summation
Asymptotic Behavior
Nonlinearity
Interaction

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Global existence and asymptotic behavior of solutions to the fourth order nonlinear Schrödinger type equation. / Segata, Junichi; Shimomura, Akihiro.

In: Communications in Applied Analysis, Vol. 11, No. 2, 01.04.2007, p. 169-188.

Research output: Contribution to journalArticle

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