We consider the Cauchy problem for the one dimensional nonlinear dissipative Schrödinger equation with a cubic nonlinearity λ| u| 2u, where λ∈ C with Im λ< 0. We show that a relation between L2-decay rate for the solution and a smoothness of the initial data. Our result improves the recent work of Hayashi–Li–Naumkin (Adv Math Phys Art. ID 3702738, 7, 2016) for the decay rate of L2.
ASJC Scopus subject areas
- Applied Mathematics