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arXiv · 1908.05101

Soliton solutions of the nonlinear Schr\"odinger equation with defect conditions

K. T. Gruner
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Abstract

A recent development in the derivation of soliton solutions for initial-boundary value problems through Darboux transformations, motivated to reconsider solutions to the nonlinear Schr\"odinger (NLS) equation on two half-lines connected via integrable defect conditions. Thereby, the Darboux transformation to construct soliton solutions is applied, while preserving the spectral boundary constraint with a time-dependent defect matrix. In this particular model, $N$-soliton solutions vanishing at infinity are constructed. Further, it is proven that solitons are transmitted through the defect independently of one another.

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K. T. Gruner. 2019-08-14. Soliton solutions of the nonlinear Schr\"odinger equation with defect conditions. https://arxiv.org/abs/1908.05101

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