Applications of cnoidal and snoidal wave solutions via optimal system of subalgebras for a generalized extended (2+1)-D quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering.

Abstract

The nonlinear evolution equations have a wide range of applications, more precisely in physics, biology, chemistry and engineering fields. This domain serves as a point of interest to a large extent in the world's mathematical community. Thus, this paper purveys an analytical study of a generalized extended (2+1)- dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering. The Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the model. We further reduce the equation using the subalgebras obtained. Besides, more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion technique. Consequently, we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright, dark, periodic (cnoidal and snoidal), compact-type as well as singular solitons. The applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time, are outlined with suitable diagrams. This can be of interest to oceanographers and ocean engineers for future analysis. Furthermore, to visualize the dynamics of the results found, we present the graphic display of each of the solutions. Conclusively, we construct conservation laws of the understudy equation via the application of Noether's theorem.