Propagation properties of dipole-managed solitons through an inhomogeneous cubic–quintic–septic medium

The presence of inhomogeneities in an optical nonlinear material may significantly change the physical features of propagating envelopes. In this paper, we discuss the propagation of very short pulses in an inhomogeneous highly nonlinear single-mode fiber within the context of a higher-order nonlinear Schrödinger equation exhibiting a diversity of important physical effects and spatially inhomogeneous coefficients. Additional effects to the cubic model include distributed third- and fourth-order dispersion, self-steepening, self-frequency shift due to stimulated Raman scattering, quintic–septic non-Kerr nonlinearities, the time derivative of non-Kerr nonlinear terms, and gain or loss term. By adopting a complex amplitude ansatz solution that is composed of the product of bright and dark solitary waves, the exact dipole soliton solution is derived. The conditions on the inhomogeneous fiber parameters for the existence of dipole structures are also reported. It is shown that the soliton dynamics in the inhomogeneous fiber media can be effectively controlled by choosing the parameters associated with the group velocity and the gain or loss term appropriately. Different from the higher-order nonlinear Schrödinger equation with constant coefficients, dipole solitons in variable-coefficient model have shown novel and interesting features. Finally, the stability of the dipole solitons is discussed numerically under finite initial perturbations.