Symmetry analysis and invariant solutions of generalized coupled Zakharov-Kuznetsov equations using optimal system of Lie subalgebra

Abstract

Abstract This research focuses on the examination of nonlinear evolution equations, with a specific emphasis on the generalized coupled Zakharov-Kuznetsov (CZK) equations serving as a primary example. Given the wide application of classical Lie symmetry methods in this field, our study employs a Lie symmetry analysis to investigate the CZK equations, as detailed in this research. Our methodology involves the construction of a nine-dimensional optimal system by leveraging the fundamental elements of the Lie algebra. Subsequently, we apply similarity reductions to the equations using each subalgebra. The resulting invariant solutions find diverse applications within the realm of physics and can also be adapted to solve a broad range of related nonlinear evolution equations. We meticulously validate all these solutions through a straightforward verification process. To enhance our comprehension of the physical implications of these solutions, we employ Mathematica simulations to visually represent various solution scenarios. Additionally, to preserve conservation laws, we incorporate Ibragimov’s novel conservation law theorem as a crucial component of our analysis.