The nonlinear Schrödinger equation with t-periodic data: I. Exact results

2014/12/31 by J. Lenells, A. S. Fokas · 1 citation
Mathematics · Physics and Astronomy · #math.AP #nlin.SI #msc:35Q55 #msc:37K15

paper · pdf · doi:10.1098/rspa.2014.0925

23 pages

arxiv created 2015/09/19 · arxiv updated 2016/02/17

Abstract

We consider the nonlinear Schrödinger equation on the half-line with a given Dirichlet (Neumann) boundary datum which for large t tends to the periodic function g₀^b(t) (g₁^b(t)). Assuming that the unknown Neumann (Dirichlet) boundary value tends for large t to a periodic function g₁^b(t) (g₀^b(t)), we derive an easily verifiable condition that the functions g₀^b(t) and g₁^b(t) must satisfy. Furthermore, we introduce two different methods, one based on the formulation of a Riemann-Hilbert problem, and one based on a perturbative approach, for constructing g₁^b(t) (g₀^b(t)) in terms of g₀^b(t) (g₁^b(t)).

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