A study of (3+1)-dimensional generalized Korteweg-de Vries- Zakharov-Kuznetsov equation via Lie symmetry approach

Abstract

In this work, we analytically examine a (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation (gKdV-ZKe). Solutions of this equation, including a non-topological soliton, are obtained by Lie symmetry reductions and direct integration. Moreover, Kudryashov’s method is utilized to generate some closed-form solutions of the equation. Furthermore, cnoidal and snoidal periodic wave solutions are displayed for a special case of the gKdV-ZKe. The obtained solutions are presented graphically. Conclusively, we provide conservation laws of gKdV-ZKe by engaging Noether’s theorem.

Keywords

• (3+1)-Dimensional generalized Korteweg-de Vries- Zakharov-Kuznetsov equation
• Lie symmetries
• Closed-form solutions
• Kudryashov’s method
• Conservation laws