Gauge equivalence theory of the noncompact Ishimori model and the Davey–Stewartson equation

Abstract

The gauge equivalence between a noncompact version of the Ishimori spin model and the Davey–Stewartson equation is established. Explicit relationships connecting the corresponding two sets of fields involved in these systems are obtained via any pair of complex functions satisfying an equation of the Schrödinger type for a free particle. Using these formulas, two examples of classes of nontrivial exact singular solutions to the Davey–Stewartson equation are given. One of them is of the closed stringlike type, while the other is doubly periodic and is expressed in terms of Riemann theta functions. The role played by the symmetry group associated with the gauge equivalent equations under consideration is also clarified.