Existence and stability of standing waves of fourth order nonlinear Schrödinger type equation related to vortex filament

Masaya Maeda, Jun Ichi Segata

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

In this paper, we study the fourth order nonlinear Schrödinger type equation (4NLS) which is a generalization of the Fukumoto-Moffatt [5] model that arising in the context of the motion of a vortex filament. Firstly, we mention the existence of standing wave solution and the conserved quantities. We next investigate the case that the equation is completely integrable and show that the standing wave obtained in [20] is orbitally stable in Sobolev spaces Hm with m ∈ N. Further, we show that the completely integrable equation is ill-posed in Hs with s ∈(-1/2,1/2) by following Kenig-Ponce-Vega [13].

Original languageEnglish
Pages (from-to)1-14
Number of pages14
JournalFunkcialaj Ekvacioj
Volume54
Issue number1
DOIs
Publication statusPublished - 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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