Construction of solutions of the defocusing nonlinear Schrödinger equation with asymptotically time-periodic boundary values

2019/07/03 by Fromm, Samuel
#35Q15 #35Q55 #41A60 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1907.01998

Abstract

We study the defocusing nonlinear Schrödinger 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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