抄録
The quaternionic KP hierarchy is the integrable hierarchy of p.d.e obtained by replacing the complex numbers with the quaternions in the standard construction of the KP hierarchy and its solutions; it is equivalent to what is often called the Davey-Stewartson II hierarchy. This article studies its relationship with the theory of conformally immersed tori in the 4-sphere via quaternionic holomorphic geometry. The Sato-Segal-Wilson construction of KP solutions is adapted to this setting and the connection with quaternionic holomorphic curves is made. We then compare three different notions of “spectral curve”: the QKP spectral curve; the Floquet multiplier spectral curve for the related Dirac operator; and the curve parameterising Darboux transforms of a conformal 2-torus in the 4-sphere.
