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Averaging principle for the Schrödinger equations

The first author is supported by NSFC Grant 11601073 and the Fundamental Research Funds for the Central Universities, the second author is supported by NSFC Grant 11171132.
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  • Averaging principle for the cubic nonlinear Schrödinger equations with rapidly oscillating potential and rapidly oscillating force are obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between nonlinear Schrödinger equation and its averaged equation. Furthermore, the existence of almost periodic solution for cubic nonlinear Schrödinger equations is also investigated.

    Mathematics Subject Classification: Primary:35B35, 35B40, 34C27;Secondary:34D20, 34D35, 58J37.


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