Dispersive dark optical soliton with Tzitzéica type nonlinear evolution equations arising in nonlinear optics

Abstract

A improvement of the expansion methods namely the improved $$\tan \left( \varPhi (\xi )/2\right)$$ -expansion method for solving the Tzitzeica type nonlinear evolution equations is proposed. In this work, the dispersive optical solitons that are governed by the Tzitzeica type nonlinear evolution equations. As a result, many new and more general exact travelling wave solutions are obtained including periodic function solutions, soliton-like solutions and trigonometric function solutions. The exact particular solutions containing four types hyperbolic function solution, trigonometric function solution, exponential solution and rational solution. We obtained the further solutions comparing with other methods. Recently this method is developed for searching exact travelling wave solutions of nonlinear partial differential equations. Abundant exact travelling wave solutions including solitons, kink, periodic and rational solutions have been found. These solutions might play important role in engineering fields. It is shown that this method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving the nonlinear problems.