Dynamics of dipole solitons on a continuous-wave background in an inhomogeneous nonlinear medium with higher-order dispersion

In this paper, the dynamics of ultrashort light pulses inside an inhomogeneous optical medium that displays all orders of dispersion up to the fourth order as well as self-steepening, self-frequency shift, and linear gain or loss is investigated. By adopting a novel approach of the amplitude function derived from the trial equation method, three types of dipole solitons are discovered. Unlike conventional dipole solitons obtained in Kerr-type media, this new soliton structure is embedded within a continuous-wave (cw) background, which influences its propagation properties. Also, the dynamic behaviors of these new soliton pulses are thoroughly explored based on the modulation of medium and pulse parameters. The results show that the shape and dynamics of the dipole-pulses on a cw background can be controlled efficiently by choosing the gain or loss and the inter-modal dispersion functions appropriately. Besides, the study conducts numerical exploration into the collision dynamics involving two and three adjacent similar solitons impacted by the inhomogeneity of medium. Finally, the stability of the dipole soliton solution on a cw background is numerically studied under the finite perturbations.