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 Kortewegde 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.

Shifted nonlocal Kundu type equations: Soliton solutions

“…If k 1 = ξ 1 +iµ 1 , ξ 1 = 0 they are all different complex valued solutions. In addition to that we obtain the same real-valued solutions |q(x, t)| 2 given by (66) and (70) for the complex shifted nonlocal space-time reversal KN equation (46) for β = − 1 2 .…”

“…giving m 1 = −ω 1 . Hence one-soliton solution of the complex shifted nonlocal space-time reversal CLL equation (46)…”

“…We have also studied shifted nonlocal NLS and MKdV equations and found one-and two-soliton solutions of these equations by the Hirota method in [45]. In [46], the authors considered space-time shifted nonlocal NLS and mKdV hierarchies and find their solutions by double Wronskians.…”

Solutions to nonlocal nonisospectral (2+1)-dimensional breaking soliton equations

“…While the reverse-(x, y) type nonlocal reduction is just admitted by the NBS-AKNS (1.2). In recent paper [30], several novel integrable nonlocal systems, including the shifted PT symmetric and the shifted time delay nonlocal NLS equations, were proposed and have attracted more and more attention [31,32]. How to extend the results in the present paper to the shifted space-time nonlocal isospectral and nonisospectral (2+1)-dimensional breaking soliton equations is an interesting questions worth consideration.…”

Bright–dark solitons in the space-shifted nonlocal coupled nonlinear Schrödinger equation

“…The higher-order soliton solutions of Eq. ( 1) were investigated by using the bilinear method [23,24].…”