Propagation of kinks embedded in nonlocal periodic waves in the inhomogeneous fiber with higher-order effect

When employing ultrashort pulses to realize the transmission of higher-bit-rate solitons, the solitons become shorter. Under these circumstances, the higher-order nonlinear Schrödinger equation needs to be utilized to describe the situation. In this article, we first verify the conditions for the generation of nonlocal symmetry in the higher-order variable-coefficient nonlinear Schrödinger equation, which contains third-order dispersion and time-delay correlation in the cubic term, via the Painlevé truncation expansion. After localizing the nonlocal symmetry into a local one, the Lie point symmetry reduction is introduced to construct the interaction solutions between kinks and nonlocal waves. Finally, the propagation of kinks on nonlocal waves, as well as the influence of higher-order dispersion and time-delay correlation on kinks in the higher-order nonlinear Schrödinger equation, are analyzed.