Abstract:We consider the initial value problem for the nonlinear Schrödinger equation satisfying the strong dissipative condition Iλ<0 and Iλ>p-1/2pRλ in one space dimension. Our purpose in this paper is to study how the gain coefficient μ(t) and strong dissipative nonlinearity λvp-1v affect solutions to the nonlinear Schrödinger equation for large initial data. We prove global existence of solutions and present some time decay estimates of solutions for large initial data.
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