Smoothing effect and large time behavior of solutions to Schrödinger equations with nonlinearity of integral type

T. Ozawa; Y. Yamazaki

doi:10.1142/S0219199704001458

Smoothing effect and large time behavior of solutions to Schrödinger equations with nonlinearity of integral type

T. Ozawa^*, Y. Yamazaki

^*Corresponding author for this work

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

3 Citations (Scopus)

Abstract

We study the smoothing effect in space and asymptotic behavior in time of solutions to the Cauchy problem for the nonlinear Schrödinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. A detailed description is given on the phase modification of scattering solutions by taking into account the long range effect of the interaction.

Original language	English
Pages (from-to)	681-703
Number of pages	23
Journal	Communications in Contemporary Mathematics
Volume	6
Issue number	4
DOIs	https://doi.org/10.1142/S0219199704001458
Publication status	Published - 2004 Aug
Externally published	Yes

Keywords

Nonlinear Schrödinger equation
scattering

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1142/S0219199704001458

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title = "Smoothing effect and large time behavior of solutions to Schr{\"o}dinger equations with nonlinearity of integral type",

abstract = "We study the smoothing effect in space and asymptotic behavior in time of solutions to the Cauchy problem for the nonlinear Schr{\"o}dinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. A detailed description is given on the phase modification of scattering solutions by taking into account the long range effect of the interaction.",

keywords = "Nonlinear Schr{\"o}dinger equation, scattering",

author = "T. Ozawa and Y. Yamazaki",

year = "2004",

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doi = "10.1142/S0219199704001458",

language = "English",

volume = "6",

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AU - Ozawa, T.

AU - Yamazaki, Y.

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N2 - We study the smoothing effect in space and asymptotic behavior in time of solutions to the Cauchy problem for the nonlinear Schrödinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. A detailed description is given on the phase modification of scattering solutions by taking into account the long range effect of the interaction.

AB - We study the smoothing effect in space and asymptotic behavior in time of solutions to the Cauchy problem for the nonlinear Schrödinger equation with interaction described by the integral of the intensity with respect to one direction in two space dimensions. A detailed description is given on the phase modification of scattering solutions by taking into account the long range effect of the interaction.

KW - Nonlinear Schrödinger equation

KW - scattering

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JO - Communications in Contemporary Mathematics

JF - Communications in Contemporary Mathematics

IS - 4

ER -

Smoothing effect and large time behavior of solutions to Schrödinger equations with nonlinearity of integral type

Abstract

Keywords

ASJC Scopus subject areas

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