Exact Solutions and Conservation Laws of the Modified Kortweg-de Vries-Zakharov-Kuznetsov (KdV-ZK) Equation

In this paper we obtain novell solutions of the modified Kortwegde Vries- Zakharov-Kuznetsov equation by employing the Lie group analysis and the (G′/G)-expansion method. The solutions to be obtained are solitary wave, perodic and rational solutions. Utilizing the Lie group analysis, the the modified Kortweg-de Vries- Zakharov-Kuznetsov equation is integrated. The Lie symmetry technique is distinct from the conventional integrability approaches, which also include Hirota's bilinear method and the multiple exp-function method,among others. The solutions capture the limiting behavior of problems that are far from their intial or boundary conditions. The conservation laws for the underlying equation are also derived by using the multiplier method. The precise solutions provided in this work are anticipated to act as a starting point for numerical simulations of the underlying equation. Furthermore we intend to construct further physical solutions of interest by employing the conservation laws reported here in this paper and these results will be reported elsewhere.