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arXiv · 2107.04183

Solutions to integrable space-time shifted nonlocal equations

Shi-min Liu·Jing Wang·Da-jun Zhang
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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.

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Shi-min Liu, Jing Wang, Da-jun Zhang. 2021-07-09. Solutions to integrable space-time shifted nonlocal equations. https://doi.org/10.1016/s0034-4877(22)00023-4

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