Electron. J. Diff. Eqns., Vol. 2007(2007), No. 61, pp. 1-10.

Blow-up solutions for N coupled Schrodinger equations

Jianqing Chen, Boling Guo

Abstract:
It is proved that blow-up solutions to N coupled Schrodinger equations
$$ i\varphi_{jt} + \varphi_{jxx} + \mu_j|\varphi_j|^{p-2}\varphi_j +\sum_{k\neq j,\;k=1}^N\beta_{kj}|\varphi_k|^{p_k}|\varphi_j|^{p_j-2} \varphi_j=0 $$
exist only under the condition that the initial data have strictly negative energy.

Submitted May 29, 2006. Published April 22, 2007.
Math Subject Classifications: 35Q55, 35B35.
Key Words: Blow-up solutions; coupled Schrodinger equations.

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Jianqing Chen
Department of Mathematics, Fujian Normal University
Fuzhou 350007, China
Institute of Applied Physics and Computational Mathematics
PO Box 8009, Beijing 100088, China
email: jqchen@fjnu.edu.cn
  Boling Guo
Institute of Applied Physics and Computational Mathematics
PO Box 8009, Beijing 100088, China
email: gbl@mail.iapcm.ac.cn

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