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arXiv · 2605.08926

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

Metin Gürses·Aslı Pekcan
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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.

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Metin Gürses, Aslı Pekcan. 2026-05-09. Multi-place shifted nonlocal reductions of a multi-component AKNS system. https://arxiv.org/abs/2605.08926

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