Multi-place shifted nonlocal reductions of a multi-component AKNS system
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915997592584192 |
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| author | Gürses, Metin Pekcan, Aslı |
| author_facet | Gürses, Metin Pekcan, Aslı |
| contents | Starting from a multi-component AKNS system, we obtain new shifted nonlocal nonlinear Schrödinger equations. We find 13 different shifted nonlocal nonlinear Schrödinger equations with two-place nonlocalities and 10 shifted nonlocal nonlinear Schrödinger 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 Schrödinger 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_08926 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Multi-place shifted nonlocal reductions of a multi-component AKNS system Gürses, Metin Pekcan, Aslı Exactly Solvable and Integrable Systems Starting from a multi-component AKNS system, we obtain new shifted nonlocal nonlinear Schrödinger equations. We find 13 different shifted nonlocal nonlinear Schrödinger equations with two-place nonlocalities and 10 shifted nonlocal nonlinear Schrödinger 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 Schrödinger 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. |
| title | Multi-place shifted nonlocal reductions of a multi-component AKNS system |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2605.08926 |