Robin boundary condition and shock problem for the focusing nonlinear Schrödinger equation

2014/12/24 by Spyridon Kamvissis, Dmitry Shepelsky, Kamvissis, Spyridon +4
Mathematics · Physics and Astronomy · #35B40 #35Q15 #35Q51 #35Q55 #37Q15 #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP #msc:35B40 #msc:35Q15 #msc:35Q51 #msc:35Q55 #msc:37Q15 #nlin.SI

paper · pdf · doi:10.48550/arxiv.1412.7636

25 pages

arxiv created 2014/12/24 · openalex publication_date 2014/12/24 · arxiv updated 2014/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the initial boundary value (IBV) problem for the focusing nonlinear Schrödinger equation in the quarter plane x>0,t>0 in the case of periodic initial data (at t=0) and a Robin boundary condition at x=0. Our approach is based on the simultaneous spectral analysis of the Lax pair equations combined with symmetry considerations for the corresponding Riemann-Hilbert problems. A connection between the original IBV problem and an associated initial value (IV) problem is established.

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