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Abstract <p> Soliton equations with self-consistent sources (SESCSs) have extensive applications in physics. In this paper, we derive the Lakshmanan–Porsezian–Daniel equation with self-consistent sources (LPD-SCS). We construct <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(N\)</EquationSource> </InlineEquation>-fold Darboux transformations for SESCSs and explicitly obtain soliton solutions and breather solutions for LPD-SCS. Moreover, we construct the generalized Darboux transformations (GDT) for the LPD-SCS and obtain rogue wave solutions. The propagation of solutions for the LPD-SCS is influenced by the arbitrary function <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(C(t)\)</EquationSource> </InlineEquation> related to the time variable <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(t\)</EquationSource> </InlineEquation>. We demonstrate such influence in this research. We also analyze the correlation between constant parameters and the propagation characteristics of solutions. </p>

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Soliton, breather, and rogue wave for the Lakshmanan–Porsezian–Daniel equation with self-consistent sources

  • 期刊论文

  • 发表日期：

    2025年12月23日

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  • Fei Li,
  • Yehui Huang,
  • Yuqin Yao

摘要

Abstract

Soliton equations with self-consistent sources (SESCSs) have extensive applications in physics. In this paper, we derive the Lakshmanan–Porsezian–Daniel equation with self-consistent sources (LPD-SCS). We construct \(N\) -fold Darboux transformations for SESCSs and explicitly obtain soliton solutions and breather solutions for LPD-SCS. Moreover, we construct the generalized Darboux transformations (GDT) for the LPD-SCS and obtain rogue wave solutions. The propagation of solutions for the LPD-SCS is influenced by the arbitrary function \(C(t)\) related to the time variable \(t\) . We demonstrate such influence in this research. We also analyze the correlation between constant parameters and the propagation characteristics of solutions.