Modified scattering operator for the derivative nonlinear Schrodinger equation

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

Research output: Contribution to journalArticleResearchpeer-review

7 Citations (Scopus)

Abstract

We consider the derivative nonlinear Schrodinger 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,?+? to the neighborhood of the origin in H1,?, where ? > 1 2 and ? > 0 is small. The weighted Sobolev space is defined by Hm,s = ? L2; (1+x2) s 2 (1-?2x ) m2 ? 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

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