Scattering problem for the supercritical nonlinear schrödinger equation in 1d

Nakao Hayashi; Pavel I. Naumkin

doi:10.1619/fesi.58.451

Scattering problem for the supercritical nonlinear schrödinger equation in 1d

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

Abstract

We consider the one dimensional nonlinear Schrödinger equation iu_t+u_xx/2 =f(u),x ∈ R, t> 0,u(0,x) =u₀(x),x ∈ R, with a super critical nonlinearity f(u) = ∑_j≠0f_j(u), and f_j(u) are such thatf_j(u) = λ_j|u|^σ_j^−ju^j, where λ_j ∈ C, σ_j > 3. We prove the existence of the scattering operator in the weighted Sobolev spaces.

Original language	English
Pages (from-to)	451-470
Number of pages	20
Journal	Funkcialaj Ekvacioj
Volume	58
Issue number	3
DOIs	https://doi.org/10.1619/fesi.58.451
Publication status	Published - 2015 Dec 26
Externally published	Yes

Keywords

Asymptotic behavior in time
Nonlinear schrödinger
Power nonlinearity
Scattering operator

ASJC Scopus subject areas

Analysis
Algebra and Number Theory
Geometry and Topology

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10.1619/fesi.58.451

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abstract = "We consider the one dimensional nonlinear Schr{\"o}dinger equation iut+uxx/2 =f(u),x ∈ R, t> 0,u(0,x) =u0(x),x ∈ R, with a super critical nonlinearity f(u) = ∑j≠0fj(u), and fj(u) are such thatfj(u) = λj|u|σj−juj, where λj ∈ C, σj > 3. We prove the existence of the scattering operator in the weighted Sobolev spaces.",

keywords = "Asymptotic behavior in time, Nonlinear schr{\"o}dinger, Power nonlinearity, Scattering operator",

author = "Nakao Hayashi and Naumkin, {Pavel I.}",

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T1 - Scattering problem for the supercritical nonlinear schrödinger equation in 1d

AU - Hayashi, Nakao

AU - Naumkin, Pavel I.

PY - 2015/12/26

Y1 - 2015/12/26

N2 - We consider the one dimensional nonlinear Schrödinger equation iut+uxx/2 =f(u),x ∈ R, t> 0,u(0,x) =u0(x),x ∈ R, with a super critical nonlinearity f(u) = ∑j≠0fj(u), and fj(u) are such thatfj(u) = λj|u|σj−juj, where λj ∈ C, σj > 3. We prove the existence of the scattering operator in the weighted Sobolev spaces.

AB - We consider the one dimensional nonlinear Schrödinger equation iut+uxx/2 =f(u),x ∈ R, t> 0,u(0,x) =u0(x),x ∈ R, with a super critical nonlinearity f(u) = ∑j≠0fj(u), and fj(u) are such thatfj(u) = λj|u|σj−juj, where λj ∈ C, σj > 3. We prove the existence of the scattering operator in the weighted Sobolev spaces.

KW - Asymptotic behavior in time

KW - Nonlinear schrödinger

KW - Power nonlinearity

KW - Scattering operator

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JF - Funkcialaj Ekvacioj

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Scattering problem for the supercritical nonlinear schrödinger equation in 1d

Abstract

Keywords

ASJC Scopus subject areas

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