The Cauchy Problem for the Hyperbolic-Elliptic Ishimori System and Schrodinger Maps

Authors

Carlos Kenig, University of Chicago
Andrea Nahmod, University of Massachusetts AmherstFollow

Publication Date

2005

Journal or Book Title

Nonlinearity

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.

Comments

DOI 10.1088/0951-7715/18/5/007

Pages

1987-2009

Volume

18

Issue

5

Recommended Citation

Kenig, Carlos and Nahmod, Andrea, "The Cauchy Problem for the Hyperbolic-Elliptic Ishimori System and Schrodinger Maps" (2005). Nonlinearity. 740.
Retrieved from https://scholarworks.umass.edu/math_faculty_pubs/740