q-Deformed solitary pulses in the higher-order nonlinear Schrödinger equation with cubic-quintic nonlinear terms

We investigate the existence and propagation properties of deformed solitary pulses in a non-Kerr medium described by the higher-order nonlinear Schrödinger equation with cubic-quintic nonlinear terms and third-order dispersion. Two different types of exact analytical q-deformed soliton solutions have been derived by means of the ansatz method. The results show that both width and amplitude of the soliton structures are influenced by the deformed factor. It is found that the introduced deformed factor lets the soliton solution deviates from the standard profile. The requirements on the parameters of the non-Kerr material for the existence of these localized structures are presented. By employing numerical simulations, we demonstrate the stability of these deformed soliton solutions under the finite perturbations. Finally, the collision between similar soliton pulses is also investigated. •The q-deformed solitary waves described by the higher-order nonlinear Schrödinger equation with cubic-quintic nonlinear non-Kerr terms are found for the first time.•Two new closed-form soliton solutions are generated using the ansatz method.•The deformation factor q acts as a parameter defining a family of solutions for the same characteristics of the material medium.•The dynamics and stability characteristics of these new solitons are discussed.•The stable propagation over long distance even in the presence of external perturbation is checked.