The Cauchy problem for the hyperbolic–elliptic Ishimori system and Schrödinger maps*

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Published 10 June 2005 • 2005 IOP Publishing Ltd and London Mathematical Society
, , Citation Carlos E Kenig and Andrea R Nahmod 2005 Nonlinearity 18 1987 DOI 10.1088/0951-7715/18/5/007

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Author affiliations

1 School of Mathematics, Institute for Advanced Study, Princeton, NJ 08540, USA

2 Department of Mathematics, University of Chicago, Chicago, IL 60637, USA

3 Department of Mathematics and Statistics, Lederle GRT, University of Massachusetts, Amherst, MA 01003-4515, USA

Dates

  1. Received 8 February 2005
  2. Published

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0951-7715/18/5/1987

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.

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Footnotes

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10.1088/0951-7715/18/5/007