Twistor reductions of the KdV hierarchy

JOURNAL OF GEOMETRY AND PHYSICS

卷:59

Article

Mo, M. Y.

关键词: Twistor geometry;    Painleve hierarchy;    Isomonodromic deformation;   

DOI  :  10.1016/j.geomphys.2008.10.009

来源: Elsevier

【 摘 要 】

It is known that the KdV hierarchy admits symmetry reductions that give rise to hierarchies of integrable ODE. In the simplest case of the KdV equation, such reductions give rise to the Painleve I and Painleve 11 equations. In [L.J. Mason, N.M.J. Woodhouse, Integrability, Self-Duality, and Twistor Theory, in: London Mathematical Society Monographs New Series, vol. 15, Oxford University Press, Oxford, 1996], a twistor description of these similarity reductions was constructed in terms of invariant vector bundles in the twistor space. In this paper we generalize this construction to the case of the KdV hierarchy to obtain the twistor spaces of the Painleve I and Painleve 11 hierarchy as twistor reductions of the KdV hierarchy. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

Free