Decay estimate and asymptotic behavior of small solutions to Schrödinger equations with subcritical dissipative nonlinearity

Abstract

This manuscript presents some results on the decay estimate and asymptotic behavior of small solutions to the Cauchy problem of 1D Schrödinger equations with a sub-critical dissipative nonlinearity. Our aim is to determine the explicit lower bound of the nonlinear power for which certain a priori estimate of the solution works well.