Large Time Asymptotics for the Fractional Order Cubic Nonlinear Schrödinger Equations

Nakao Hayashi; Pavel I. Naumkin

doi:10.1007/s00023-016-0502-9

Large Time Asymptotics for the Fractional Order Cubic Nonlinear Schrödinger Equations

Nakao Hayashi, Pavel I. Naumkin

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

7 Citations (Scopus)

Abstract

We consider the Cauchy problem for the nonlinear Schrödinger equations of fractional order (Formula presented.) where F(u) is the cubic nonlinearity F(u)=λ|u|²u with λ∈ R. We find the large time asymptotics of solutions to the Cauchy problem. We use the factorization technique similar to that developed for the Schrödinger equation.

Original language	English
Pages (from-to)	1025-1054
Number of pages	30
Journal	Annales Henri Poincare
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/s00023-016-0502-9
Publication status	Published - 2017 Mar 1
Externally published	Yes

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Nuclear and High Energy Physics
Mathematical Physics

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10.1007/s00023-016-0502-9

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title = "Large Time Asymptotics for the Fractional Order Cubic Nonlinear Schr{\"o}dinger Equations",

abstract = "We consider the Cauchy problem for the nonlinear Schr{\"o}dinger equations of fractional order (Formula presented.) where F(u) is the cubic nonlinearity F(u)=λ|u|2u with λ∈ R. We find the large time asymptotics of solutions to the Cauchy problem. We use the factorization technique similar to that developed for the Schr{\"o}dinger equation.",

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N2 - We consider the Cauchy problem for the nonlinear Schrödinger equations of fractional order (Formula presented.) where F(u) is the cubic nonlinearity F(u)=λ|u|2u with λ∈ R. We find the large time asymptotics of solutions to the Cauchy problem. We use the factorization technique similar to that developed for the Schrödinger equation.

AB - We consider the Cauchy problem for the nonlinear Schrödinger equations of fractional order (Formula presented.) where F(u) is the cubic nonlinearity F(u)=λ|u|2u with λ∈ R. We find the large time asymptotics of solutions to the Cauchy problem. We use the factorization technique similar to that developed for the Schrödinger equation.

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Large Time Asymptotics for the Fractional Order Cubic Nonlinear Schrödinger Equations

Abstract

ASJC Scopus subject areas

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