Diverse general solitary wave solutions and conserved currents of a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science

This article presents an analytical investigation performed on a generalized geophysical Korteweg–de Vries model with nonlinear power law in ocean science. To start with, achieving diverse solitary wave solutions to the generalized power‐law model involves using wave transformation, which reduces the model to a nonlinear ordinary differential equation. A direct integration approach is adopted to construct solutions in the beginning. This brings the emergence of interesting solutions like non‐topological solitons, trigonometric functions, exponential functions, elliptic functions, and Weierstrass functions in general structures. Besides, in a bid to secure more general exact solutions to the model, one adopts the extended Jacobi elliptic function expansion technique (for some specific cases of ). Thus, various cnoidal, snoidal, and dnoidal wave solutions to the understudied model are attained. The copolar trio explicated in a tabular form reveals that these solutions can be relapsed to various hyperbolic and trigonometric functions under certain criteria. Additionally, diverse graphical exhibitions of the dynamical attributes of the gained results are presented in a bid to have a sound understanding of the physical phenomena of the underlying model. Later, one gives the conserved vectors of the aforementioned equation by employing the standard multiplier approach.