Solutions to integrable space-time shifted nonlocal equations

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 Schrödinger and modified Korteweg-de Vries hierarchies and the semi-discrete nonlinear Schrödinger 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.

16 pages

References in corpus (2)

• The Fokas-Lenells equations: Bilinear approach
• Integrable nonlocal asymptotic reductions of physically significant nonlinear equations

Cited by in corpus (3)

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• The Method of ${\mathcal{M}}_n$-Extension: The KdV Equation