Modified scattering operator for the derivative nonlinear schrödinger equation

Zihua Guo, Nakao Hayashi, Yiquan Lin, Pavel I. Naumkin

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We consider the derivative nonlinear Schrödinger equation i∂tu+ 1 2 ∂2x u = i∂x(|u|2u), t R, x R. Our purpose is to prove that the modified scattering operator is defined as a map from the neighborhood of the origin in H1,α+γ to the neighborhood of the origin in H1,α, where α > 1 2 and γ > 0 is small. The weighted Sobolev space is defined by Hm,s = {φ L2; (1+x2) s 2 (1-∂2x ) m2 φ L2 ≤ ∞}.

Original languageEnglish
Pages (from-to)3854-3871
Number of pages18
JournalSIAM Journal on Mathematical Analysis
Volume45
Issue number6
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Derivative nonlinear Schrödinger equation
  • Modified scatttering operator

ASJC Scopus subject areas

  • Analysis
  • Computational Mathematics
  • Applied Mathematics

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