Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches
Analysis of PDEs
2020-07-03 v1 Mathematical Physics
Algebraic Geometry
math.MP
Exactly Solvable and Integrable Systems
Abstract
We apply the GBDT version of the B\"acklund-Darboux transformation to the nonlocal NLS (focusing and defocusing cases). The matrix case is included and solutions in the form of rectangular matrix functions are dealt with. The wave function is also constructed explicitly. Families of explicit examples are considered in detail. Some initial results and representations for the more complicated algebro-geometric solutions are obtained as well.
Keywords
Cite
@article{arxiv.1806.05019,
title = {Explicit solutions for nonlocal NLS: GBDT and algebro-geometric approaches},
author = {J. Michor and A. L. Sakhnovich},
journal= {arXiv preprint arXiv:1806.05019},
year = {2020}
}