Nonexistence of Small, Smooth, Time-periodic, Spatially Periodic Solutions for Nonlinear Schrödinger Equations
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چکیده
We study the question of nonexistence of small spatially periodic, timeperiodic solutions for cubic nonlinear Schrödinger equations. We prove that for almost any value in a bounded set of possible temporal periods, there is an amplitude threshold, below which any initial value is not the initial value for a time-periodic solution. The proof requires a certain level of Sobolev regularity on solutions. The methods used are not based on any special structure of the nonlinear Schrödinger equation, and can be applied more generally.
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تاریخ انتشار 2017