Exploration of different multi-peak solitons and vibrant breather type waves’ solutions of nonlinear Schrödinger equations with advanced dispersion and cubic–quintic nonlinearity, unveiling their applications

Abstract

Abstract The nonlinear Schrödinger equations (NLSEs) of higher order illustrate the transmission of extremely short light pulses in fiber optics. In this manuscript, we employ the two-variable (1/G, G′/G)-expansion technique to construct bright and multi-peak solitons, periodic multi-solitons, breather type solitary waves, periodic peakon solitons, and other wave solutions of higher-order NLSE in mono-mode optical fiber and generalized NLSE with cubic–quintic nonlinearity. The two-variable (1/G, G′/G)-expansion method is a generalization of the (G′/G)-expansion method, offering a more robust mathematical tool for solving various nonlinear partial differential equations (PDEs) in mathematical physics. We also analyze the characteristics of waves conducive to the formation of bright–dark and other soliton forms within this medium. Additionally, we provide graphical representations of the obtained results to visually depict the dynamical models under consideration. Our findings highlight the potency, reliability, and versatility of the proposed technique, which holds promise for solving a wide array of similar models encountered in applied sciences and engineering.