We study the initial value problem for the Ishimori system. Elliptic-hyperbolic and hyperbolic-elliptic cases were treated by inverse scattering techniques [6, 7], . Elliptic-elliptic and hyperbolic-elliptic cases were studied in  without using inverse scattering techniques. In the previous paper  we proved the global existence of small solutions to the Ishimori and the Davey-Stewartson systems in the elliptic-hyperbolic and hyperbolic-hyperbolic cases under exponential decay on the data. Our purpose in this paper is to remove that condition in the case of the Ishimori system.
"Global existence of small solutions to the Ishimori system without exponential decay on the data." Differential Integral Equations 9 (6) 1183 - 1195, 1996.