General multi-soliton and higher-order soliton solutions for a novel nonlocal Lakshmanan–Porsezian–Daniel equation

The inverse scattering transformation for a novel nonlocal Lakshmanan–Porsezian–Daniel (LPD) equation with rapidly decaying initial data is studied in the framework of Riemann–Hilbert problem. Firstly, integrable LPD corresponding to $$3\times 3$$ Lax pair proposed. Secondly, process left-right matrix Riemann–Hilbert(RH) problem constructed. analytical properties and symmetry relations Jost functions are considerably different from local ones. Due special equation, zeros RHP purely imaginary or occur pairs. With types configuration zeros, soliton formula provided rich dynamical behaviors three kinds multi-solitons demonstrated. Third, by technique adding perturbed parameters limiting process, higher-order solitons exhibited. Lastly, plots diverse various solutions combinations following zeros: simple pairs non-purely displayed.