The robust inverse scattering method for focusing Ablowitz-Ladik equation on the non-vanishing background

In this paper, we consider the robust inverse scattering method for the Ablowitz-Ladik (AL) equation on the non-vanishing background, which can be used to deal with arbitrary-order poles on the branch points and spectral singularities in a unified way. The Darboux matrix is constructed with the aid of loop group method and considered within the framework of robust inverse scattering transform. Various soliton solutions are constructed without using the limit technique. These solutions include general soliton, breathers, as well as high order rogue wave solutions. (C) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper considers the robust inverse scattering method for the Ablowitz-Ladik equation on the non-vanishing background, which deals with arbitrary-order poles on the branch points and spectral singularities in a unified way. The Darboux matrix is constructed with the loop group method within the framework of robust inverse scattering transform, and various soliton solutions are constructed without using the limit technique, including general solitons, breathers, and high order rogue wave solutions.