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.

中文翻译：

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散焦 Lakshmanan-Porsezian-Daniel 方程的色散冲击波结构分析

通过有限间隙积分理论，我们研究了散焦Lakshmanan-Porsezian-Daniel (LPD)方程。同时，我们推导了单相周期解的简并形式。此外，通过黎曼不变量参数化的Whitham调制方程，我们得到了色散激波的基本结构和组合结构。