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

T. Ozawa, Y. Yamazaki

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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 languageEnglish
Pages (from-to)681-703
Number of pages23
JournalCommunications in Contemporary Mathematics
Volume6
Issue number4
DOIs
Publication statusPublished - 2004 Aug 1

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Keywords

  • Nonlinear Schrödinger equation
  • scattering

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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