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By constructing a kind of generalized Lie algebra, based on generalized Tu scheme, a new ( 2 + 1 )-dimensional mKdV hierarchy is derived which popularizes the results of ( 1 + 1 )-dimensional integrable system. Furthermore, the ( 2 + 1 )-dimensional mKdV equation can be applied to describe the propagation of the Rossby solitary waves in the plane of ocean and atmosphere, which is different from the ( 1 + 1 )-dimensional mKdV equation. By virtue of Riccati equation, some solutions of ( 2 + 1 )-dimensional mKdV equation are obtained. With the help of solitary wave solutions, similar to the fiber soliton communication, the chirp effect of Rossby solitary waves is discussed and some conclusions are given.

( 2 + 1 )-Dimensional mKdV Hierarchy and Chirp Effect of Rossby Solitary Waves