Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation

In this paper, a nonlocal Lakshmanan-Porsezian-Daniel equation is investigated with the help of the binary Darboux transformation method and asymptotic analysis. Nonlocality of that equation has been reflected in that the solutions of that equation at the location zeta depend on both the local solution at zeta and the nonlocal solution at -zeta, where zeta is the retarded time coordinate. We derive the formulas of the Nth-order solutions through the obtained binary Darboux transformation, where N is a positive integer. Under certain conditions, the first-order periodic waves and solitons are obtained, e.g., degenerate solitons, dark-dark solitons, bright-bright solitons and dark-bright solitons. Interactions between/among the dark solitons, bright solitons and periodic wave are discussed and graphically illustrated. We discuss the modulation instability of that equation. (c) 2022 Elsevier B.V. All rights reserved.

Automated summary

In this paper, a nonlocal Lakshmanan-Porsezian-Daniel equation is studied using the binary Darboux transformation method and asymptotic analysis. The nonlocality of the equation is reflected in the dependence of the solutions on both the local and nonlocal solutions at different positions. The formulas for Nth-order solutions are derived using the binary Darboux transformation, and first-order periodic waves and solitons are obtained under certain conditions. The interactions between dark solitons, bright solitons, and periodic waves are discussed, as well as the modulation instability of the equation.