The investigation of exact solutions of Korteweg-de vries equation with dual power law nonlinearity using the exp_a and exp (− Φ (ξ)) methods

Abstract

In this work, the methodologies of the exp${}_a$ and exp$(-\mathrm{\Phi }(\xi ))$ methods are used to investigate the solutions of Korteweg-de Vries (KdV) equation with dual power law nonlinearity. The obtained solutions consist of kink, anti-kink, logarithmic, trigonometric, hyperbolic and rational functions. Moreover, 3D and 2D graphics of some of these exact solutions have been plotted to visualize the underlying dynamics of proposed results.

Keywords:

• The exp${}_a$ method
• the exp$(-\mathrm{\Phi }(\xi ))$-expansion method
• KdV equation
• dual power law nonlinearity
• exact solutions

2010 Mathematics Subject Classification:

• 35

Disclosure statement

No potential conflict of interest was reported by the author(s).