Dressing a new integrable boundary of the nonlinear Schrödinger equation

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.

arXiv comment24 pages, 4 figures

References in corpus (1)

• Solitons, boundary value problems and a nonlinear method of images

Cited by in corpus (2)

• Nonlinear Schrödinger equation on the half-line without a conserved number of solitons
• On an inverse scattering transform for the nonlinear Schödinger equation on the half-line