Homotopic method of solving a class of E1 Niño/La Niña-Southern Oscillation sea--air oscillator

The EI Niño/La Niña-Southern Oscillation (ENSO) is an interannual phenomenon involved in the tropical Pacific Ocean--atmosphere interactions. In this paper, an asymptotic method of solving the nonlinear equation for the ENSO model is created. And based on a class of oscillator of the ENSO model, the approximate solution of a corresponding problem is studied by employing the method of homotopic mapping. It is proved from the results that the homotopic method can be used for analysing the sea surface temperature anomaly in the equatorial eastern Pacific and the thermocline depth anomaly of the atmosphere--ocean oscillation for the ENSO model.