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.

中文翻译：

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通过地球物理Korteweg-de Vries方程研究科里奥利对海洋流动及其分支的影响

在这项工作中，我们借助地球物理Korteweg-de Vries方程（GKdVE）研究了科里奥利对赤道地区海洋流动的影响。首先，研究了GKdVE的Lie对称性和守恒律。稍后，我们将采用有限元方法进行数值模拟。非线性孤立结构的传播，它们的相互作用和孤子的发展可以从产生的结果中看出。此外，还研究了高斯初始条件和双孔初始条件。发现如此获得的结果与可用结果完全一致。根据行波速度和科里奥利参数，对GKdVE的海洋行波进行了分叉分析。