Abundant solitary wave solutions of Gardner’s equation using new ϕ6-model expansion method

Abstract

The Gardner’s equation is the generalization of Kortweg-de Vries equation and modified Kortweg-de Vries equation having real life applications in different fields of science, such as, hydrodynamics, quantum field theory, etc. Moreover, it has applications in fluid mechanics where it explains surface and internal waves. This manuscript addresses application of the new ϕ6-model expansion method to Gardner’s equation for getting its solitary wave solutions. Such new results aid in getting noteworthy advances in various disciplines of science and technology. Periodic, kink, anti-kink, bright, dark, w-shaped and singular soliton solutions of the governing equation have been constructed. The proposed method takes into account a variety of closed form solutions using the Jacobi elliptic functions. The graphical illustration of some of the obtained solutions has been presented for a suitable choice of free parameters to depict the dynamic nature of the obtained wave solutions.

Keywords

• Expansion technique
• Nonlinear partial differential equation
• Analytical solutions
• Solitary waves