DISPERSIVE OPTICAL SOLITON PERTURBATION WITH SCHRODINGER-HIROTA EQUATION BY LIE SYMMETRY

This study investigates traveling-wave solutions of a perturbed Schrödinger-Hirota equation that includes third-order dispersion, nonlinear dispersion, intermodal dispersion, self-steepening, and selffrequency-shift terms.The complex equation is decomposed into an equivalent real coupled system, and its Lie point symmetries are determined.A compatible linear combination of the translation and phase-rotation generators yields a traveling-wave reduction, subject to an explicit relation between the phase frequency and the symmetry coefficient.For the zero integration-constant branch, the reduced nonlinear ordinary differential equation is treated with a generalized auxiliary-equation method.Hyperbolic, exponential, and Jacobi-elliptic solution families are obtained under stated nondegeneracy, reality, and denominator conditions.Their limiting behaviors distinguish kink-type, dark-type, bright-type, singular, and nonlocalized profiles.Intensity plots illustrate representative propagation morphologies but are not used as evidence of stability.