Scattering of solutions to the fourth-order nonlinear Schrödinger equation

Nakao Hayashi; Jesus A. Mendez-Navarro; Pavel I. Naumkin

doi:10.1142/S0219199715500352

Scattering of solutions to the fourth-order nonlinear Schrödinger equation

Nakao Hayashi, Jesus A. Mendez-Navarro, Pavel I. Naumkin

Research Alliance Center for Mathematical Sciences (RACMaS)

Research output: Contribution to journal › Article

3 Citations (Scopus)

Abstract

We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation i{iσtu + 1/4σ⁴_xu=|u|^p-1u,t>0,xεR,u(0,x)=u0(x),xεR, where ε C, > 4. We introduce the factorization for the free evolution group to prove the large time asymptotics of solutions.

Original language	English
Article number	1550035
Journal	Communications in Contemporary Mathematics
Volume	18
Issue number	3
DOIs	https://doi.org/10.1142/S0219199715500352
Publication status	Published - 2016 Jun 1

Keywords

Fourth-order nonlinear Schrödinger equation
Large time asymptotics

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1142/S0219199715500352

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Hayashi, N., Mendez-Navarro, J. A., & Naumkin, P. I. (2016). Scattering of solutions to the fourth-order nonlinear Schrödinger equation. Communications in Contemporary Mathematics, 18(3), [1550035]. https://doi.org/10.1142/S0219199715500352

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abstract = "We consider the Cauchy problem for the fourth-order nonlinear Schr{\"o}dinger equation i{iσtu + 1/4σ4xu=|u|p-1u,t>0,xεR,u(0,x)=u0(x),xεR, where ε C, > 4. We introduce the factorization for the free evolution group to prove the large time asymptotics of solutions.",

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AU - Mendez-Navarro, Jesus A.

AU - Naumkin, Pavel I.

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N2 - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation i{iσtu + 1/4σ4xu=|u|p-1u,t>0,xεR,u(0,x)=u0(x),xεR, where ε C, > 4. We introduce the factorization for the free evolution group to prove the large time asymptotics of solutions.

AB - We consider the Cauchy problem for the fourth-order nonlinear Schrödinger equation i{iσtu + 1/4σ4xu=|u|p-1u,t>0,xεR,u(0,x)=u0(x),xεR, where ε C, > 4. We introduce the factorization for the free evolution group to prove the large time asymptotics of solutions.

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KW - Large time asymptotics

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