【摘要】 厄尔尼诺-南方涛动是一个涉及赤道太平洋海-气交互作用的年际现象.本文的目的是创建一个求解厄尔尼诺-南方涛动模型非线性系统的渐近方法.首先利用线性齐次常微分系统的特征值理论得到了对应初值问题的解,并以此解为原系统的零次近似解,然后利用同伦映射关系式依次构造原系统的各次迭代解,最后在这基础上借助同伦映射方法研究了厄尔尼诺南方涛动系统海-气振子对应问题的渐近解,并证明了得到的渐近解的一致有效性.从得到的结果看出,同伦映射方法能够用于分析厄尔尼诺-南方涛动系统在赤道东太平洋中的海表温度异常和海-气振子的温跃层深度异常.更多还原

【Abstract】 The EI Nin?o-southern oscillation is an interannual phenomenon involved in the tropical Pacific ocean-atmosphere interactions. The aim of this paper is to create an asymptotic method of solve nonlinear equation for the EI Nin?o-southern oscillation system. Firstly, the solution to corresponding initial value problem is got by using the characteristic value theory for the linear homogeneous ordinary differential system. And this solution is a zero-th order approximation of solution to the original system. Then, the arbitrary order iterative solutions for the original system are structured with the help of homotopic mapping relational expressions successively.Finally, based on a class of oscillator for the EI Nin?o-southern oscillation system,employing the homotopic mapping method, the asymptotic solution to corresponding problem is studied. And there is proved this asymptotic solution is a uniformly valid. The results is that the homotopic mapping method can be used for analyzing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the sea-air oscillator for the EI Nin?o-southern oscillation system.更多还原