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.
Nakao Hayashi. Jean-Claude Saut. "Global existence of small solutions to the Ishimori system without exponential decay on the data." Differential Integral Equations 9 (6) 1183 - 1195, 1996. https://doi.org/10.57262/die/1367846895