中文摘要：

本文首次从带有地形的赤道大气基本方程组出发,利用浅水模式近似、半地转近似、Gardner-Morikawa变换以及摂动展开法得到了具有地形效应的赤道非线性波动振幅所满足的Korteweg-de Vries方程,并且利用Jacobi椭圆函数展开法求得非线性方程对应的周期波解和孤立波解,指出地形是产生赤道Rossby孤立波的重要因素.

英文摘要：

Nonlinear Rossby waves near equator with topography in basic shallow water model equations are studied in the present paper.The evolution of wave amplitude is characterized by a nonlinear Korteweg-de Vries equation through equatorial semigeostrophic approximation,Gardner-Morikawa transformation and perturbation expansion method.The periodic wave solution and solitary wave solution are obtained by the method of Jacobi elliptic function expansions.From the evolution equation,it is found that the effect from topography on nonlinear equatorial Rossby solitary wave is significant.