Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension

Kei Nakamura; Tohru Ozawa

doi:10.3934/dcds.2013.33.789

Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension

Kei Nakamura, Tohru Ozawa

School of Advanced Science and Engineering

Research output: Contribution to journal › Article

1 Citation (Scopus)

Abstract

We study the Cauchy problem for cubic Schrödinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L ²(R) without any approximating arguments.

Original language	English
Pages (from-to)	789-801
Number of pages	13
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	33
Issue number	2
DOIs	https://doi.org/10.3934/dcds.2013.33.789
Publication status	Published - 2013 Jan 1

Keywords

Blow-up
Nonlinear Schrödinger equations
Scattering.

ASJC Scopus subject areas

Analysis
Discrete Mathematics and Combinatorics
Applied Mathematics

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Nakamura, K., & Ozawa, T. (2013). Finite charge solutions to cubic schrödinger equations with a nonlocal nonlinearity in one space dimension. Discrete and Continuous Dynamical Systems- Series A, 33(2), 789-801. https://doi.org/10.3934/dcds.2013.33.789

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abstract = "We study the Cauchy problem for cubic Schr{\"o}dinger equations modelling ultra-short laser pulses propagating along the line. The global existence, blow-up, and scattering of solutions is described exclusively in the charge space L 2(R) without any approximating arguments.",

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