Article
The Cauchy Problem for the Hyperbolic-Elliptic Ishimori System and Schrodinger Maps
Nonlinearity
Publication Date
2005
Abstract
We show an improved local in time existence and uniqueness result for Schrödinger maps and for the hyperbolic–elliptic nonlinear system proposed by Ishimori in analogy with the two-dimensional classical continuous isotropic Heisenberg spin (2d-CCIHS) chain. The proof uses fairly standard gauge geometric tools and energy estimates in combination with Kenig's version of the Koch–Tzvetkov method, to obtain a priori estimates for classical solutions to certain dispersive equations.
Disciplines
Pages
1987-2009
Citation Information
Carlos Kenig and Andrea Nahmod. "The Cauchy Problem for the Hyperbolic-Elliptic Ishimori System and Schrodinger Maps" Nonlinearity Vol. 18 Iss. 5 (2005) Available at: http://works.bepress.com/andrea_nahmod/25/
DOI 10.1088/0951-7715/18/5/007