Lie Symmetry Analysis, Exact Solutions, and Conservation Laws of the Geophysical Korteweg–de Vries Equation - Okeke, Michael Ikechukwu; Okeke, Justina Ebele; Oraekie, Paul Anaeto (Faculty of Natural and Applied Sciences Journal of Mathematical and Statistical Computing, 2025)
The Korteweg-de Vries equation is a nonlinear PDE that is used to describe most physical systems involving dispersion, such as wave propagation, fluid dynamics, and plasma physics. In the light of the influence of coriolis effect on waves, the study of the Geophysical Korteweg-de Vries (GKdV) equation is examined. The Lie point symmetries and conservation laws of the equation are constructed and with the Lie point symmetries, a symmetry analysis is performed to reduce the equation to an integrable form. Numerical solutions of the reduced equation were considered for the travelling wave (periodic wave) of the GKdV equation for the parameters (for the coriolis effect) and (for the velocity of the wave). To examine the coriolis effect on free flow in oceans, the dynamical system analysis is applied on the GKdV equation. From the study, it is revealed that travelling wave velocity and coriolis factor have significant effects on the transmission of the periodic wave solution of the GKdV equation. The results obtained stands as a motivation to extend the method to some other nonlinear evolution equations.