Optical soliton perturbation in a log-law medium with full nonlinearity by He's semi-inverse variational principle

In this article, optical soliton solution of the non-linear Schrödinger's equation with log law non-linearity is obtained by He's variational principle. The perturbation terms that are considered are inter-modal dispersion, self-steepening term and non-linear dispersion, where the last two perturbation terms are with full non-linearity. A numerical simulation is given to complete the study.