A new three dimensional dissipative Boussinesq equation for Rossby waves and its multiple soliton solutions

Abstract A new three dimensional nonlinear dynamic theoretical model is derived from fluid mechanics system. In this paper, From the quasi-geostrophic barotropic potential vorticity equation, we obtain a dissipative Boussinesq equation by reduced perturbation method, i.e. u tt + e 1 xx 2 ( ) 3 txy 4 xxxx 5 xxyy = 0 . It emphasized that different existing equations, which describe Rossby waves in atmosphere. Moreover, explore dispersion relation of linear wave through equation. Using travelling method and simplest general solution soliton solutions are obtained successfully respectively. Finally, formation mechanism discussed multiple solutions.