The defocusing Lakshmanan–Porsezian–Daniel equation with elliptic function backgrounds: N-elliptic-dark solitons and asymptotic behaviors

By using the modified squared wavefunction approach and Darboux transformation, we derive the $N$-elliptic-dark soliton solutions for the defocusing Lakshmanan–Porsezian–Daniel equation, which describes the propagation of ultrashort optical pulses with the fourth-order dispersion, self-steepening, self-frequency, and quintic effects. In particular, we exhibit the one-, two- and three-elliptic-dark solitons as well as their asymptotic behaviors as $t\to \pm \infty$, and discuss the compression effects on the spatiotemporal distributions of the elliptic dark solitons produced by the higher-order effects.