Solitary wave solutions to Gardner equation using improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method

Abstract

In this study, the improved tan$ \left(\frac{\Omega(\Upsilon)}{2}\right) $-expansion method is used to construct a variety of precise soliton and other solitary wave solutions of the Gardner equation. Gardner equation is extensively utilized in plasma physics, quantum field theory, solid-state physics and fluid dynamics. It is the simplest model for the description of water waves with dual power law nonlinearity. Hyperbolic, exponential, rational and trigonometric traveling wave solutions are obtained. The retrieved solutions include kink solitons, bright solitons, dark-bright solitons and periodic wave solutions. The efficacy of this method is determined by the comparison of the newly obtained results with already reported results.

Keywords

• exact solutions
• solitary waves
• gardner equation
• exponential solution
• rational function
• solitons
• hyperbolic solution
• improved tan$ \left(\frac{\omega(\upsilon)}{2}\right) $-expansion method