Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation

Dexin Meng; Dexin Meng

doi:10.3934/math.2025124

AIMS Mathematics

2025, Volume 10, Issue 2: 2652-2667. doi: 10.3934/math.2025124

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Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation

Dexin Meng ^,

College of Science, China University of Petroleum, Beijing, People's Republic of China

Received: 10 October 2024 Revised: 24 January 2025 Accepted: 11 February 2025 Published: 14 February 2025
MSC : 37K40

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.
- nonlocal derivative nonlinear Schrödinger equation,
- Darboux transformation,
- Wronskian-type determinant solution
Citation: Dexin Meng. Wronskian-type determinant solutions of the nonlocal derivative nonlinear Schrödinger equation[J]. AIMS Mathematics, 2025, 10(2): 2652-2667. doi: 10.3934/math.2025124

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Abstract

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.

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