Higher-order rational solutions for a new integrable nonlocal fifth-order nonlinear Schrödinger equation

We study the soliton and rational solutions of a new integrable nonlocal fifth-order nonlinear Schrödinger (NFONLS) equation with three free parameters. In particular, the nonlocal classical NLS, nonlocal Hirota and nonlocal Lakshmanan-Porsezian-Daniel (LPD) equations can be obtained from this integrable equation by choosing appropriate parameters. The Lax pair and the generalized Darboux transformations of NFONLS are constructed for the first time, from which the Nth order soliton and rational solutions are given in matrix form, and the contour profiles and density evolutions of rational solutions are given to investigate their wave structures and dynamic properties. These results may be useful in nonlinear fiber optics and the relevant physical fields.