Solutions to integrable space-time shifted nonlocal equations

TL;DR

This paper develops a reduction technique using bilinearization and double Wronskians to derive explicit multi-soliton solutions for recently introduced integrable space-time shifted nonlocal equations, revealing shared eigenvalue distributions and new phase constraints.

Contribution

It introduces a novel reduction method based on bilinearization and double Wronskians for solving space-time shifted nonlocal integrable equations.

Findings

Shared eigenvalue distributions between shifted and unshifted equations

Space-time shifts impose new phase constraints on solutions

Explicit multi-soliton solutions derived for various 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 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.