Time Decay for Nonlinear Dissipative Schrödinger Equations in Optical Fields

We consider the initial value problem for the nonlinear dissipative Schrödinger equations with a gauge invariant nonlinearity of order for arbitrarily large initial data, where the lower bound is a positive root of for and for Our purpose is to extend the previous results for higher space dimensions concerning -time decay and to improve the lower bound of under the same dissipative condition on : and as in the previous works.

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