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

Fei Li^ab, Yehui Huang^ab, Yuqin Yao<sup>ab

a</sup> Department of Applied Mathematics, China Agricultural University, Beijing, China
^b Teaching Center of Mathematics, Tsinghua University, Beijing, China

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.

Keywords: Lakshmanan–Porsezian–Daniel equation with self-consistent sources, restricted flows, Darboux transformation, soliton solution, rogue wave, breather solution.

PACS: 02.30.lk

MSC: Partial differential equations

Received: 18.12.2024
Revised: 18.03.2025

DOI: 10.4213/tmf10874

 English version: Theoretical and Mathematical Physics, 2025, 225:3, 2188–2202

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