Abstract In this paper we investigate the instability of two-layer quasi-geostrophic model with scalar nonlinearity, which is a geophysical fluid dynamics model, and give a nonlinear stability criterion. Furthermore, the analytical solutions of the two-layer quasi-geostrophic model are obtained via the Jacobi elliptic periodic function transform method and symbolic computation. It is efficient in solving a range classes of nonlinear partial differential equations for this method. The result shows that the structure of Rossby waves is influenced by many factors such as base flow and scalar nonlinearity.

中文翻译：

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两层准地转流的孤立波及标量非线性解析解

摘要 本文研究了具有标量非线性的两层准地转模型地球物理流体动力学模型的不稳定性，并给出了非线性稳定性判据。此外，通过Jacobi椭圆周期函数变换方法和符号计算得到了两层准地转模型的解析解。用这种方法求解一系列非线性偏微分方程组是有效的。结果表明，Rossby波的结构受基流、标量非线性等多种因素的影响。