Optimal L2-decay of solutions to a nonlinear Schrödinger equation with sub-critical dissipative nonlinearity

This paper presents the optimality of decay estimate of solutions to the initial value problem of 1D-nonlinear Schrödinger equations with a sub-critical dissipative power nonlinearity. Our aim is to obtain two results. One asserts that, if a global solution decays more rapidly than t - d with d = 1 / ( p - 1 ) - 1 / 2 in L 2 , then it must be a trivial solution. The other one shows the existence of a solution decaying just at the rate of t - d in L 2 .