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- Title
NONEXISTENCE OF ASYMPTOTICALLY FREE SOLUTIONS TO NONLINEAR SCHRÖDINGER SYSTEMS.
- Authors
HAYASHI, NAKAO; CHUNHUA LI; NAUMKIN, PAVEL I.
- Abstract
We consider the nonlinear Schrödinger systems -i∂tu1 + 1/2Δu1 = F(u1, u2), i∂tu2 + 1/2Δu2 = 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.
- Subjects
NONLINEAR systems; SCHRODINGER equation; SMOOTHING (Numerical analysis); WAVE equation; INVARIANT wave equations
- Publication
Electronic Journal of Differential Equations, 2012, Vol 2012, p1
- ISSN
1550-6150
- Publication type
Article