The Cauchy problem for the Ishimori equation
The Ishimori equation, describing the two-dimensional analog of the classical continuous isotropic Heisenberg spin chain is mapped via a gauge transformation onto the Davey-Stewartson II equation for shallow watter waves. Results concerning the Cauchy problem for the Ishimori equation are obtained by exploiting this correspondence and the known results about the Cauchy problem for Davey-Stewartson II equation. In particular, conditions are given under which the Cauchy problem for the Ishimori equation is well-posed, i.e. solutions are unique and show continuous dependence upon the initial conditions.
scientific article; zbMATH DE number 944390