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arXiv · 1907.01998

Construction of solutions of the defocusing nonlinear Schr\"odinger equation with asymptotically time-periodic boundary values

Samuel Fromm
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Abstract

We study the defocusing nonlinear Schr\"odinger equation in the quarter plane with asymptotically periodic boundary values. By studying an associated Riemann-Hilbert problem and employing nonlinear steepest descent arguments, we construct solutions in a sector close to the boundary whose leading behaviour is described by a single exponential plane wave. Furthermore, we compute the subleading terms in the long time asymptotics of the constructed solutions.

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Samuel Fromm. 2019-07-03. Construction of solutions of the defocusing nonlinear Schr\"odinger equation with asymptotically time-periodic boundary values. https://arxiv.org/abs/1907.01998

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