Lie Subalgebras, Solutions and Conserved Vectors of a Nonlinear Geophysical Korteweg de Vries Equation in Ocean Physics and Nonlinear Mechanics with Power Law

Abstract Ocean physics describes the way the ocean surface layer interacts with the atmosphere and extends to the transmission of energy from ocean waves and tides to the seafloor. Hence, for the first time, this article explores the analytical study of a generalized geophysical Korteweg-de Vries equation found in ocean physics with power-law nonlinearity. The model is analyzed using the Lie group theory that ensures mapping of the existing solutions to other solutions. Initially, the calculation of the associated Lie algebra for the model is carried out in a systematic manner, after which one parameter transformation group for the algebra is derived. Besides, a one-dimensional optimal system of subalgebra is derived in a procedural manner. Sequel to this, the subalgebras and combination of the achieved symmetries are invoked in the reduction process, culminating in generating nonlinear ordinary differential equations associated with the model under study. In consequence, analytic soliton solutions, including non-topological soliton solutions and general periodic function solutions of note, in the structure of Weierstrass elliptic and Jacobi elliptic functions are obtained for the model. One of the interesting results also includes an implicit hypergeometric function solution. Additionally, numerical simulations are utilized to develop a basic understanding of the physical phenomena described by the model in ocean physics. Ultimately, conserved vectors are determined for the model by applying Ibragimov’s theorem together with Noether’s theorem.