Dynamical Analysis and Exact Solutions of a New (2+1)-Dimensional Generalized Boussinesq Model Equation for Nonlinear Rossby Waves**Supported by the National Natural Science Foundation of China under Grant Nos. 11562014, 11762011, 11671101, 71471020, 51839002; the Natural Science Foundation of Inner Mongolia under Grant No. 2017MS0108; Hunan Provincial Natural Science Foundation of China under Grant No. 2016JJ2061; the Scientific Research Fund of

Abstract

In this paper, we study the higher dimensional nonlinear Rossby waves under the generalized beta effect. Using methods of the multiple scales and weak nonlinear perturbation expansions [Q. S. Liu, et al., Phys. Lett. A 383 (2019) 514], we derive a new (2+1)-dimensional generalized Boussinesq equation from the barotropic potential vorticity equation. Based on bifurcation theory of planar dynamical systems and the qualitative theory of ordinary differential equations, the dynamical analysis and exact traveling wave solutions of the new generalized Boussinesq equation are obtained. Moreover, we provide the numerical simulations of these exact solutions under some conditions of all parameters. The numerical results show that these traveling wave solutions are all the Rossby solitary waves.