Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg–de Vries equation

Abstract

In this work, we have investigated Coriolis effect on oceanic flows in the equatorial region with the help of geophysical Korteweg-de Vries equation (GKdVE). First, Lie symmetries and conservation laws for the GKdVE have been studied. Later, we implement finite element method for numerical simulations. Propagation of nonlinear solitary structures, their interaction and advancement of solitons can be seen in the results so produced. Additionally, Gaussian initial condition and undular bore initial condition are also investigated. Results so obtained have been found in perfect agreement with the available results. Bifurcation analysis of the oceanic traveling wave of the GKdVE is presented depending on traveling wave velocity and Coriolis parameter. It is discerned that velocity of the traveling wave and Coriolis parameter affect significantly on the propagation of the nonlinear waves.

Novel travelling wave structures: few-cycle-pulse solitons and soliton molecules

“…It has been realized that there are many different types of waves in numerous media based on large universal nonlinear equations, such as the KdV equation [1], the KP equation in water surface gravity waves and plasma [2], the mKdV equation in plasma and optics [3,4], the NLS equation in nonlinear optics [5], the sine-Gordon equation in field theory [6] and biaxial ferromagnets [7], etc. Many interesting and effective methods and techniques, including the Lie point symmetry and group theory [8], the bilinear method [9], Darboux transformations and Bäcklund transformations, the Lax pair and the inverse scattering method [10], CRE [11] and CTE expand [12], etc, have been used to search for the exact solutions of the universal nonlinear equations.…”