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arXiv · 2008.03272

Dressing a new integrable boundary of the nonlinear Schr\"odinger equation

K. T. Gruner
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Abstract

We further develop the method of dressing the boundary for the focusing nonlinear Schr\"odinger 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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K. T. Gruner. 2020-08-07. Dressing a new integrable boundary of the nonlinear Schr\"odinger equation. https://arxiv.org/abs/2008.03272

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