Solitary wave solutions and other solutions for Gilson–Pickering equation by using the modified extended mapping method

Abstract

In this paper, the modified extended mapping method is applied to obtain solitary wave solutions and other solutions for the Gilson–Pickering equation which describes the wave propagation in plasma physics. Many types of solutions are obtained such as shock wave, singular waves, periodic waves, singular periodic waves, Jacobi elliptic functions, plane waves, hyperbolic waves, Weierstrass elliptic solutions and exponential type solutions. Moreover, 3D graphs of some solutions are introduced for the physical illustration.

Keywords

• Shock waves
• Exact solutions
• Gilson–Pickering equation
• Modified extended mapping method