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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:399

Article

Ozawa, Tohru²  Sunagawa, Hideaki¹ 

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

[2] Waseda Univ, Dept Appl Phys, Shinjuku Ku, Tokyo 1698555, Japan

关键词: Nonlinear Schrodinger equation;    Small data blow-up;    Hopf-Cole transformation;    Mass resonance;   

DOI  :  10.1016/j.jmaa.2012.10.003

来源: Elsevier

【 摘 要 】

We give examples of small data blow-up for a three-component system of quadratic nonlinear Schrodinger 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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free