In this paper, we investigate a (2+1)-dimensional nonlinear equation model for Rossby waves in stratified fluids. We derive a forced Zakharov–Kuznetsov(ZK)–Burgers equation from the quasi-geostrophic potential vorticity equation with dissipation and topography under the generalized beta effect, and by utilizing temporal and spatial multiple scale transform and the perturbation expansion method. Through the analysis of this model, it is found that the generalized beta effect and basic topography can induce nonlinear waves, and slowly varying topography is an external impact factor for Rossby waves. Additionally, the conservation laws for the mass and energy of solitary waves are analyzed. Eventually, the solitary wave solutions of the forced ZK–Burgers equation are obtained by the simplest equation method as well as the new modified ansatz method. Based on the solitary wave solutions obtained, we discuss the effects of dissipation and slowly varying topography on Rossby solitary ...

中文翻译：

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分层流体中Rossby波的（2 + 1）维非线性模型及其孤立解

在本文中，我们研究了分层流体中Rossby波的（2 + 1）维非线性方程模型。我们在广义β效应下，利用具有耗散和地形的拟地转势涡旋方程，并利用时空多尺度变换和摄动展开法，推导了强迫的Zakharov–Kuznetsov（ZK）–Burgers方程。通过对该模型的分析，发现广义的β效应和基本形貌可以诱发非线性波，并且缓慢变化的形貌是Rossby波的外部影响因素。另外，分析了孤立波的质量和能量守恒律。最终，通过最简单的方程方法以及新的改进的ansatz方法获得了强迫ZK-Burgers方程的孤波解。