Type: Article

Nonexistence of asymptotically free solutions to nonlinear schrodinger systems

Hayashi, Nakao; Chunhua LI; Naumkin, Pavel I.;

Abstract:

We consider the nonlinear Schrodinger systems -i partial derivative(t)u(1) + 1/2 Delta u(1) = F(u1, u2), i partial derivative(t)u(2) + 1/2 Delta u(2) - F(u1, u2) in n space dimensions, where F is a p-th order local or nonlocal nonlinearity smooth up to order p, with 1 < p <= 1 + 2/n for n >= 2 and 1 < p <= 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.