The Ward equation (a modified 2d-sigma model) is obtained by a dimension reduction and a gauge fixing from the self-dual Yang-Mills equation on $R^{2,2}$. It is an integrable non-linear wave equation in 2 space variables and one time variable. A stationary solution of the Ward equation is a harmonic map from a Riemann surface, and a solution independent of one of the space variable is a 1-d wave map. In this talk, I will discuss various results by Ward, Ioannidou, Shatah-Strauss, Uhlenbeck, Dai and myself on soliton interactions, and on periodic and
homoclinic orbits.