Novel singular solitons in optical metamaterials for self-steepening effect

We consider the evolution of ultrashort pulses in metamaterials wherein the pulse propagation is governed by the generalized nonlinear Schrödinger equation with higher-order effects such as pseudo-quintic nonlinearity and self-steepening effect. We present three new types of exact singular soliton-like solutions for the model in the presence of the self-steepening term, whose phase chirping varies as a function of the pulse intensity. The obtained results indicate that the parameters of solutions are directly related the self-steepening parameter. Parametric conditions on physical parameters for the existence of the novel structures are also presented. Particular cases are discussed.