Differential and Integral Equations

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

Nakao Hayashi and Jean-Claude Saut

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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

Permanent link to this document
https://projecteuclid.org/euclid.die/1367846895

Mathematical Reviews number (MathSciNet)
MR1409922

Zentralblatt MATH identifier
0879.34053

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35D05 35E99: None of the above, but in this section 81T99: None of the above, but in this section

Citation

Hayashi, Nakao; Saut, Jean-Claude. Global existence of small solutions to the Ishimori system without exponential decay on the data. Differential Integral Equations 9 (1996), no. 6, 1183--1195. https://projecteuclid.org/euclid.die/1367846895


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