Modified scattering operator for the derivative nonlinear Schrodinger equation

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

doi:10.1137/12089956X

Modified scattering operator for the derivative nonlinear Schrodinger equation

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

Research output: Contribution to journal › Article › Research › peer-review

10 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 language	English
Pages (from-to)	3854 - 3871
Number of pages	18
Journal	SIAM Journal on Mathematical Analysis
Volume	45
Issue number	6
DOIs	https://doi.org/10.1137/12089956X
Publication status	Published - 2013
Externally published	Yes

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title = "Modified scattering operator for the derivative nonlinear Schrodinger equation",

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 ? ? .",

author = "Zihua Guo and Nakao Hayashi and Yiquan Lin and Naumkin, {Pavel I}",

year = "2013",

doi = "10.1137/12089956X",

language = "English",

volume = "45",

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T1 - Modified scattering operator for the derivative nonlinear Schrodinger equation

AU - Guo, Zihua

AU - Hayashi, Nakao

AU - Lin, Yiquan

AU - Naumkin, Pavel I

PY - 2013

Y1 - 2013

N2 - 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 ? ? .

AB - 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 ? ? .

UR - http://epubs.siam.org.ezproxy.lib.monash.edu.au/doi/pdf/10.1137/12089956X

U2 - 10.1137/12089956X

DO - 10.1137/12089956X

M3 - Article

SN - 0036-1410

VL - 45

SP - 3854

EP - 3871

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

IS - 6

ER -

Modified scattering operator for the derivative nonlinear Schrodinger equation

Abstract

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