Dressing a new integrable boundary of the nonlinear Schrödinger equation

2020/08/07 by K. T. Gruner, Gruner, K. T. · 1 citation
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.2008.03272

24 pages, 4 figures

arxiv created 2020/08/07 · arxiv updated 2020/08/10

Abstract

We further develop the method of dressing the boundary for the focusing nonlinear Schrödinger equation (NLS) on the half-line to include the new boundary condition presented by Zambon. Additionally, the foundation to compare the solutions to the ones produced by the mirror-image technique is laid by explicitly computing the change of scattering data under the Darboux transformation. In particular, the developed method is applied to insert pure soliton solutions.

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