Dark spatial solitary waves in a cubic-quintic-septimal nonlinear medium

Abstract

We consider the evolution of light beams in nonlinear media exhibiting nonlinearities up to the seventh order wherein the beam propagation is governed by the cubic-quintic-septimal nonlinear Schr\odinger equation. An exact analytic solution that describes dark solitary wave propagation is obtained, based on a special ansatz. Unlike the well-known $\text{tanh}$-profile dark soliton in Kerr media, the present one has a functional form given in terms of ``${\text{sech}}^{2/3}$''. The requirements concerning the optical material parameters for the existence of this localized structure are discussed. This propagating solitary wave exists due to a balance among diffraction, cubic, quintic, and septimal nonlinearities. We also investigate its stability under initial pertubations by employing numerical simulations. The modulational stability of the continuous-wave background, which supports the dark soliton, is also studied analytically. Collisions between stable dark solitons are finally investigated.