The quaternionic KP hierarchy and conformally immersed 2-tori in the 4-sphere. (English) Zbl 1237.35141
This work is concerned with the quaternionic KP hierarchy, which is equivalent to 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. Then the author compares 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.
Reviewer: Guanggan Chen (Chengdu)
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 14H70 | Relationships between algebraic curves and integrable systems |
| 53A30 | Conformal differential geometry (MSC2010) |
| 53C42 | Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) |
Keywords:
integrable systems; conformally immersed tori; quaternionic holomorphic curves; spectral curvesReferences:
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