We study asymptotic behavior in time of solutions to nonlinear Schrödinger equations in three space dimensions with quadratic nongauge invariant nonlinearities. Due to the oscillation properties of such nonlinearities the time decay estimates are faster comparing with the case of guge invariant nonlinearities. We prove the existence of solutions to the final problem and large time asymptotics.
@article{1597,
title = {Existence of asymptotically free solutions for quadratic nonlinear Schr\"odinger equations in 3d},
journal = {CUBO, A Mathematical Journal},
volume = {9},
year = {2007},
language = {en},
url = {http://dml.mathdoc.fr/item/1597}
}
Hayashi, Nakao; Naumkin, Pavel l. Existence of asymptotically free solutions for quadratic nonlinear Schrödinger equations in 3d. CUBO, A Mathematical Journal, Tome 9 (2007) . http://gdmltest.u-ga.fr/item/1597/