Traveling Wave Solutions to the Nonlinear Evolution Equation Using Expansion Method and Addendum to Kudryashov’s Method

Abstract

The inspection of wave motion and propagation of diffusion, convection, dispersion, and dissipation is a key research area in mathematics, physics, engineering, and real-time application fields. This article addresses the generalized dimensional Hirota–Maccari equation by using two different methods: the exp(−φ(ζ)) expansion method and Addendum to Kudryashov’s method to obtain the optical traveling wave solutions. By utilizing suitable transformations, the nonlinear pdes are transformed into odes. The traveling wave solutions are expressed in terms of rational functions. For certain parameter values, the obtained optical solutions are described graphically with the aid of Maple 15 software.

Keywords

• optical soliton solution
• simple algebraic direct method
• nonlinear evolution equations
• nonlinear Hirota–Maccari equation
• addendum to Kudryashov’s method