English

Solutions to integrable space-time shifted nonlocal equations

Exactly Solvable and Integrable Systems 2022-05-18 v1

Abstract

In this paper we present a reduction technique based on bilinearization and double Wronskians (or double Casoratians) to obtain explicit multi-soliton solutions for the integrable space-time shifted nonlocal equations introduced very recently by Ablowitz and Musslimani in [Phys. Lett. A, 2021]. Examples include the space-time shifted nonlocal nonlinear Schr\"odinger and modified Korteweg-de Vries hierarchies and the semi-discrete nonlinear Schr\"odinger equation. It is shown that these nonlocal integrable equations with or without space-time shift(s) reduction share same distributions of eigenvalues but the space-time shift(s) brings new constraints to phase terms in solutions.

Keywords

Cite

@article{arxiv.2107.04183,
  title  = {Solutions to integrable space-time shifted nonlocal equations},
  author = {Shi-min Liu and Jing Wang and Da-jun Zhang},
  journal= {arXiv preprint arXiv:2107.04183},
  year   = {2022}
}

Comments

16 pages

R2 v1 2026-06-24T04:01:38.898Z