Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 61, pp. 1-10.

Title: Blow-up solutions for N coupled Schrodinger equations

Authors: Jianqing Chen (Fujian Normal Univ., Fuzhou, China)
         Boling Guo (Institute of Applied Phys. and Math., Beijing, China)     

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.