非线性光学晶格中的梯度流方法

Abstract

Abstract:

In this paper, we study the existence of the steady state solutions for a classical Schrödinger equation in nonlinear optical lattices by means of gradient flow method. We first establish the existence of a global solution of the governing parabolic equation. Then we prove the convergence of the global solution to an equilibrium (i.e., a steady state solution in optical lattices model) as time goes to infinity. Furthermore, we provide an estimate on the convergence rate by using the Łojasiewicz-Simon inequality.

Key words: Gradient flow method, Schrödinger Equation, Łojasiewicz-Simon inequality, Steady state solutions

CLC Number:

O175.26

Ruifeng Zhang,Nan Liu. Gradient Flow Method in Nonlinear Optical Lattices[J].Acta mathematica scientia,Series A, 2019, 39(5): 1170-1182.

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References 42

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Gradient Flow Method in Nonlinear Optical Lattices

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