Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 162, pp. 1-14.

Title: Nonexistence of asymptotically free solutions to nonlinear 
       Schrodinger systems

Authors: Nakao Hayashi (Osaka Univ., Toyonaka, Japan)
         Chunhua Li  (Yanbian Univ., Yanji, China)
	 Pavel I. Naumkin (UNAM Campus Morelia, Mexico)

Abstract:
 We consider the nonlinear Schrodinger systems
 $$\displaylines{
 -i\partial _tu_1+\frac{1}{2}\Delta u_1=F( u_1,u_2), \cr
  i\partial _tu_2+\frac{1}{2}\Delta u_2=F( u_1,u_2)
  }$$
 in n space dimensions, where F is a  p-th order local or nonlocal
 nonlinearity smooth up to order p, with $1<p\leq 1+\frac{2}{n}$ for
 $n\geq 2$ and $1<p\leq 2$ for n=1. These systems are related to higher
 order nonlinear dispersive wave equations. We prove the non existence of
 asymptotically free solutions in the critical and sub-critical cases.

Submitted November 17, 2011. Published September 21, 2012.
Math Subject Classifications: 35Q55.
Key Words: Dispersive nonlinear waves; asymptotically free solutions.