A class of recharge–discharge oscillator model for the El Ni？o/Southern Oscillation （ENSO） is considered. A stable limit cycle is obtained by transforming the ENSO model into the van der Pol-Duffing equation. We proved that there exists periodic oscillations in the ENSO recharge–discharge oscillator model.
By using the Jacobi elliptic-function method, this paper obtains the periodic solutions for coupled integrable dispersionless equations. The periodic solutions include some kink and anti-kink solitons.
