Differential and Integral Equations

Global existence of small solutions to the Ishimori system without exponential decay on the data

Abstract

We study the initial value problem for the Ishimori system. Elliptic-hyperbolic and hyperbolic-elliptic cases were treated by inverse scattering techniques [6, 7], [9]. Elliptic-elliptic and hyperbolic-elliptic cases were studied in [8] without using inverse scattering techniques. In the previous paper [4] 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.

Article information

Source
Differential Integral Equations, Volume 9, Number 6 (1996), 1183-1195.

Dates
First available in Project Euclid: 6 May 2013