Conservation Laws of Space-Time Fractional mZK Equation for Rossby Solitary Waves with Complete Coriolis Force

摘要

The study of Rossby solitary waves are of great significance in physical oceanography, atmospheric physics, water conservancy project, military and communications engineering, etc. All the time, in the study of Rossby solitary waves, people have been focusing on integer order models. Recently, fractional calculus has become a new research hotspot, and it has opened a new door to research atmospheric and ocean. Thus, the fractional order model has the potential value in the study of Rossby solitary waves. In the present paper, according to the quasi-geostrophic potential vorticity equation with the complete Coriolis force, we get a new integer order mZK equation. Using the semi-inverse method and the fractional variational principle, the space-time fractional mZK(STFmZK) equation is obtained. To better understand the property of Rossby solitary waves, we study Lie symmetry analysis, nonlinear self-adjointness, similarity reduction by applying the STFmZK equation. In the end, the conservation and Caputo fractional derivative are discussed, respectively.