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.

24 pages, 4 figures

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