Small data blow-up for a system of nonlinear Schrödinger equations

Tohru Ozawa; Hideaki Sunagawa

doi:10.1016/j.jmaa.2012.10.003

Small data blow-up for a system of nonlinear Schrödinger equations

Tohru Ozawa, Hideaki Sunagawa^*

^*Corresponding author for this work

School of Advanced Science and Engineering

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

22 Citations (Scopus)

Abstract

We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

Original language	English
Pages (from-to)	147-155
Number of pages	9
Journal	Journal of Mathematical Analysis and Applications
Volume	399
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2012.10.003
Publication status	Published - 2013 Mar 1

Keywords

Hopf-Cole transformation
Mass resonance
Nonlinear Schrödinger equation
Small data blow-up

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2012.10.003

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abstract = "We give examples of small data blow-up for a three-component system of quadratic nonlinear Schr{\"o}dinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.",

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AU - Sunagawa, Hideaki

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AB - We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrödinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

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KW - Mass resonance

KW - Nonlinear Schrödinger equation

KW - Small data blow-up

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Small data blow-up for a system of nonlinear Schrödinger equations

Abstract

Keywords

ASJC Scopus subject areas

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