The soliton solutions for an integrable nonlocal reverse space–time fifth-order nonlinear Schrödinger equation by the inverse scattering transform

Abstract

This paper begins by deducing a reverse space–time nonlocal fifth-order nonlinear Schrödinger (NLS) equation, which arises from a simple yet significant symmetry reduction of the corresponding local system. Following this, the determinant form of $N$ soliton solutions is thoroughly constructed based on established Gelfand–Levitan–Marchenko(GLM) equation. As a typical application, some exact solutions are derived, including one-soliton, two-soliton, and three-soliton solutions. The dynamical properties of these solutions are further explored and visualized through graphical analysis. Moreover, the integrability of the equation is established by presenting an infinite set of conserved densities. It is particularly noteworthy that we also present the expression for the three-soliton solution, which represents an unprecedented achievement in this field.