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In the paper, beginning from the quasi-geostrophic potential vorticity equation with the dissipation and thermal forcing in stratified fluid, by employing multiscale analysis and perturbation method, we derive a forced 3-D Zakharov Kuznetsor (ZK)-Burgers equation describe the propagation of the Rossby solitary waves within the fractional derivative. The exact solutions are given by virtue of the (G’/G)-expansion method to analyze the excitation effect of thermal forcing on the Rossby waves.

A forced 3-D time fractional ZK-Burgers model for Rossby solitary waves with dissipation and thermal forcing