Inverse scattering transforms of the inhomogeneous fifth-order nonlinear Schrödinger equation with zero/nonzero boundary conditions

Abstract

Abstract The present work studies the inverse scattering transforms (IST) of the inhomogeneous fifth-order nonlinear Schrödinger (NLS) equation with zero boundary conditions (ZBCs) and nonzero boundary conditions (NZBCs). Firstly, the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent’s series for the first time. Then, by combining with the robust IST, the Riemann-Hilbert (RH) problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed. Furthermore, based on the resulting RH problem, some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation. Finally, some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.