English

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 m1×m2m_1 \times m_2 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}
}