The exact solutions to a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel equation

In this paper, we study a new type space reverse nonlocal Lakshmanan–Porserzian–Daniel (LPD) equation which can be derived from the two-component LPD system with a special reduction. We construct the multi-fold binary Darboux transformation for the nonlocal equation. The advantage of the binary Darboux transformation is that it provide a short-cut to construct explicit formulas for the solutions of nonlocal equation with zero and non-zero background conditions, such as the interaction bright soliton wave which can degenerate into the one bright wave having a sudden phase shift, the bound state bright wave which looks like a breather wave, the multi-humps bright wave, the interaction breather wave and the resonance breather wave. We find that these solutions exhibit various dynamic evolutions, and most of the collisions between the waves in these solutions are inelastic.