A fractional geoKdV model in higher dimensional oceanic flows and its applications in geophysics

In this manuscript, our goal is to investigate effects of Coriolis constant attribute on obtained solutions for the geoKdV equation. Two effective techniques will be employed to unveil diverse manifestations of soliton behaviors produced by the simple equation method and the modified generalized exponential rational function technique (mGERFT). Our suggested procedures are implemented for obtaining various types of exact solutions of geoKdV equation. These methods allow us to obtain solutions formulated in terms of special functions, which are very useful in many different branches of mathematical physics. Furthermore, our research will be presented novel and distinctive arrangements of soliton behaviors derived from this model, offering perspectives on real-world uses in the field of geophysics. As a result, we deliver accurate wave solutions for bright and dark bell-shaped waves, multiple single solitons, exponential solutions and periodic waves profile. Using the computational program Maple, we have produced multiple 2D plots and 3D plots with contour lines of our obtained solutions. These structures can also characterize various explanations for other models in the purviews of nonlinear science and engineering.