Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation
A nonlocal derivative nonlinear Schrödinger (DNLS) equation is analytically studied in this paper. By constructing Darboux transformations (DTs) of arbitrary order, new determinant solutions of the nonlocal DNLS equation in the form of Wronskian-type are derived from both zero and nonzero seed solut...
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AIMS Press
2025-02-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2025124 |
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| author | Dexin Meng |
| author_facet | Dexin Meng |
| author_sort | Dexin Meng |
| collection | DOAJ |
| description | A nonlocal derivative nonlinear Schrödinger (DNLS) equation is analytically studied in this paper. By constructing Darboux transformations (DTs) of arbitrary order, new determinant solutions of the nonlocal DNLS equation in the form of Wronskian-type are derived from both zero and nonzero seed solutions. Periodic solitons are obtained with different parameter choices. When one eigenvalue tends to another one, generalized DTs are constructed, leading to rogue waves. Due to complex parametric constraints, the derived solutions may have singularities. Despite this, the work presented in this paper can still provide a valuable reference for the study of nonlocal integrable systems. |
| format | Article |
| id | doaj-art-b70932e546fd480b9c7668230f4e345b |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | AIMS Press |
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| series | AIMS Mathematics |
| spelling | doaj-art-b70932e546fd480b9c7668230f4e345b2025-08-20T02:08:20ZengAIMS PressAIMS Mathematics2473-69882025-02-011022652266710.3934/math.2025124Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equationDexin Meng0College of Science, China University of Petroleum, Beijing, People's Republic of ChinaA nonlocal derivative nonlinear Schrödinger (DNLS) equation is analytically studied in this paper. By constructing Darboux transformations (DTs) of arbitrary order, new determinant solutions of the nonlocal DNLS equation in the form of Wronskian-type are derived from both zero and nonzero seed solutions. Periodic solitons are obtained with different parameter choices. When one eigenvalue tends to another one, generalized DTs are constructed, leading to rogue waves. Due to complex parametric constraints, the derived solutions may have singularities. Despite this, the work presented in this paper can still provide a valuable reference for the study of nonlocal integrable systems.https://www.aimspress.com/article/doi/10.3934/math.2025124nonlocal derivative nonlinear schrödinger equationdarboux transformationwronskian-type determinant solution |
| spellingShingle | Dexin Meng Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation AIMS Mathematics nonlocal derivative nonlinear schrödinger equation darboux transformation wronskian-type determinant solution |
| title | Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation |
| title_full | Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation |
| title_fullStr | Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation |
| title_full_unstemmed | Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation |
| title_short | Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation |
| title_sort | wronskian type determinant solutions of the nonlocal derivative nonlinear schrodinger equation |
| topic | nonlocal derivative nonlinear schrödinger equation darboux transformation wronskian-type determinant solution |
| url | https://www.aimspress.com/article/doi/10.3934/math.2025124 |
| work_keys_str_mv | AT dexinmeng wronskiantypedeterminantsolutionsofthenonlocalderivativenonlinearschrodingerequation |