Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields - Nakao Hayashi; Chunhua Li; Pavel I. Naumkin (Advances in Mathematical Physics)
We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearity λup-1u of order pn<p≤1+2/n for arbitrarily large initial data, where the lower bound pn is a positive root of n+2p2-6p-n=0 for n≥2 and p1=1+2 for n=1. Our purpose is to extend the previous results for higher space dimensions concerning L2-time decay and to improve the lower bound of p under the same dissipative condition on λ∈C: Im⁡ λ<0 and Im⁡ λ>p-1/2pRe λ as in the previous works.