Abstract
In this paper, we investigate a reputed nonlinear partial differential equation (NLPDE) known as geophysical Korteweg-de Vries (GPKdV) equation. We implement a renowned Unified method (UM) of nonlinear (NL) sciences for the extraction of polynomial and rational function solutions of GPKdV equation, which degenarate to various wave solutions like solitary, soliton (dromions) and elliptic wave solutions. Further more, for the analysis of the integrability of our governing model, we apply Painlevé (P) algorithm to check the singularities structure of the model. The fulfillment of all the requirements of the P test indicates the solvability of the governing equation with the help of inverse scattering transformation (IST) or some linear techniques. Moreover, we calculate conservation laws (CLs) in polynomial form as conserved fluxes and densities by implementing dilation symmetry. We utilize Euler and Homotopy operators for the evaluation of the intended conserved quantities.
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