Abstract: The EI Ni$\tilde{\rm n}$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 Ni$\tilde{\rm n}$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 Ni$\tilde{\rm n}$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 Ni$\tilde{\rm n}$o-southern oscillation system.

Key words: nonlinear, El Ni$\tilde{\rm n}$o-southern oscillation, sea-air oscillator