Multi-place shifted nonlocal reductions of a multi-component AKNS system

TL;DR

This paper derives new shifted nonlocal nonlinear Schrödinger equations from a multi-component AKNS system, finds explicit one-soliton solutions, and analyzes their singularity structures and parameter conditions.

Contribution

It introduces 23 new shifted nonlocal NLS equations with different nonlocalities and provides explicit soliton solutions via Hirota's method.

Findings

13 equations with two-place nonlocalities identified

10 equations with four-place nonlocalities identified

Nonsingular one-soliton solutions are obtained and analyzed

Abstract

Starting from a multi-component AKNS system, we obtain new shifted nonlocal nonlinear Schr\"{o}dinger equations. We find 13 different shifted nonlocal nonlinear Schr\"{o}dinger equations with two-place nonlocalities and 10 shifted nonlocal nonlinear Schr\"{o}dinger equations with four-place nonlocalities. We first obtain one-soliton solutions of the multi-component AKNS system by the Hirota method. Applying the shifted nonlocal reduction formulas to this solution, we obtain one-soliton solutions for the shifted nonlocal nonlinear Schr\"{o}dinger equations. In cases yielding nontrivial solutions, we discuss the singularity structures of the solutions and show that the one-soliton solutions we obtain are nonsingular for certain values of the parameters. We plot representative nonsingular solutions obtained for admissible parameter values.