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The principal purpose of this paper is to examine the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity which governs the propagation of dispersive pulses in optical fibers by proposing and using a direct algebraic form of the enhanced modified extended tanh expansion method for the first time. Our aim is not only restricted to obtaining different and more soliton solutions by proposed method for the first time in this study, but also includes examining the effect of the coefficients of self-steepening and nonlinear dispersion terms to the soliton propagation in the investigated problem.

Utilizing a traveling wave transformation, the perturbed Schrödinger–Hirota equation with the effect of spatio-temporal dispersion and Kerr law nonlinearity can be transformed into an nonlinear ordinary differential equation (NODE). Then, the NODE is convert …