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

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.