Implicit quiescent optical soliton perturbation having nonlinear chromatic dispersion and generalized temporal evolution with Kudryashov’s forms of self-phase modulation structure by Lie symmetry

The article investigates the nonlinear Schrödinger’s equation using nonlinear chromatic dispersion and a generalised temporal evolution. Lie symmetry retrieves quiescent optical solitons from the model. The solutions are implicit, with quadratures and expressed in terms of elliptic and periodic functions. The six self-phase modulation structures examined in this study were first introduced by Kudryashov.