English

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

Mathematical Physics 2020-08-10 v1 math.MP

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.

Keywords

Cite

@article{arxiv.2008.03272,
  title  = {Dressing a new integrable boundary of the nonlinear Schr\"odinger equation},
  author = {K. T. Gruner},
  journal= {arXiv preprint arXiv:2008.03272},
  year   = {2020}
}

Comments

24 pages, 4 figures