Dispersive shock wave structure analysis for the defocusing Lakshmanan−Porsezian−Daniel equation

Via the finite-gap integration theory, we study the defocusing Lakshmanan-Porsezian-Daniel (LPD) equation. Meanwhile, we derive the degenerate forms for the single-phase periodic solution. In addition, we obtain the basic and combined structures of the dispersive shock wave through the Whitham modulation equation parameterized by the Riemann invariant.