Homoclinic and heteroclinic solutions of the nonlinear Schrödinger equation with a complex Wadati potential

Abstract

Stationary solutions asymptoting to nonlinear plane waves of the nonlinear Schrödinger equation with a PT-symmetric, complex linear potential are characterized. The potential includes both a spatially varying gain-loss profile and a repulsive real part, generated by a Wadati potential function,that support the existence of homoclinic and heteroclinic solutions that asymptote to the same or different, respectively, nonlinear plane waves in the far field. Asymptotic analysis and numerical simulations are used to examine solution existence, bifurcations, and structure. Such solutions play an important role in resonant nonlinear wave generation of dispersive media with localized gain and loss.