The Cauchy problem of the Ward equation

We generalize the results of [J. Villarroel, The inverse problem for Ward's system, Stud. Appl. Math. 83 (1990) 211–222; A.S. Fokas, T.A. Ioannidou, The inverse spectral theory for the Ward equation and for the 2+1 chiral model, Comm. Appl. Anal. 5 (2001) 235–246; B. Dai, C.L. Terng, K. Uhlenbeck, On the space–time Monopole equation, arXiv:math.DG/0602607] to study the inverse scattering problem of the Ward equation with non-small data and solve the Cauchy problem of the Ward equation with a non-small purely continuous scattering data.