K. T. Gruner | Searcharxiv

arXiv2020

Dressing a new integrable boundary of the nonlinear Schrödinger equation

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.

math-ph↗

arXiv2020

Soliton solutions of the nonlinear Schrödinger equation with defect conditions

A recent development in the derivation of soliton solutions for initial-boundary value problems through Darboux transformations, motivated to reconsider solutions to the nonlinear Schrödinger (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.

math-ph↗