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Novel Particular Solutions, Breathers, and Rogue Waves for an Integrable Nonlocal Derivative Nonlinear Schrödinger Equation

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  • Yali Shen
  • Ruoxia Yao
  • Wen-Xiu Ma

Abstract

A determinant representation of the n-fold Darboux transformation for the integrable nonlocal derivative nonlinear Schödinger (DNLS) equation is presented. Using the proposed Darboux transformation, we construct some particular solutions from zero seed, which have not been reported so far for locally integrable systems. We also obtain explicit breathers from a nonzero seed with constant amplitude, deduce the corresponding extended Taylor expansion, and obtain several first-order rogue wave solutions. Our results reveal several interesting phenomena which differ from those emerging from the classical DNLS equation.

Suggested Citation

  • Yali Shen & Ruoxia Yao & Wen-Xiu Ma, 2022. "Novel Particular Solutions, Breathers, and Rogue Waves for an Integrable Nonlocal Derivative Nonlinear Schrödinger Equation," Advances in Mathematical Physics, Hindawi, vol. 2022, pages 1-9, January.
    • Handle: RePEc:hin:jnlamp:7670773
    DOI: 10.1155/2022/7670773
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    Cited by:

    1. Wen-Xiu Ma, 2024. "A Generalized Hierarchy of Combined Integrable Bi-Hamiltonian Equations from a Specific Fourth-Order Matrix Spectral Problem," Mathematics, MDPI, vol. 12(6), pages 1-12, March.

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