从地球流体中非线性波动所满足的方程经行波变换所得的平面自治动力系统出发 ,利用微分方程几何理论 ,揭示了地球流体中几种非线性波动均具有周期解 ,而不存在孤波解的普遍性质。采用在平面自治系统的平衡点附近作 Tay-lor展开方法 ,论证了分式简谐函数是有限振幅波解的一般形式的结论。 Based on the planar autonomous dynamical system obtained by the traveling wave transformation of the equations satisfied by the nonlinear fluctuations in the earth fluid and using the geometric theory of differential equations, it is revealed that some nonlinear oscillations in the earth fluid have periodic solutions without solitary wave solutions The universal nature of By using the Tay-lor expansion method near the equilibrium point of the planar autonomous system, the conclusion that the fractional harmonic function is the general form of the finite amplitude solution is given.