Integrability via geometry: dispersionless differential equations in three and four dimensions

Autor:	Calderbank, David M. J., Kruglikov, Boris
Rok vydání:	2016
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry Nonlinear Sciences - Exactly Solvable and Integrable Systems 35L70 37K10 53C28 58J60 14D21 32L25 35A30 35Q75 53C25 58A20
Druh dokumentu:	Working Paper
Popis:	We prove that the existence of a dispersionless Lax pair with spectral parameter for a nondegenerate hyperbolic second order partial differential equation (PDE) is equivalent to the canonical conformal structure defined by the symbol being Einstein-Weyl on any solution in 3D, and self-dual on any solution in 4D. The first main ingredient in the proof is a characteristic property for dispersionless Lax pairs. The second is the projective behaviour of the Lax pair with respect to the spectral parameter. Both are established for nondegenerate determined systems of PDEs of any order. Thus our main result applies more generally to any such PDE system whose characteristic variety is a quadric hypersurface. Comment: 26 pages, v2 substantially expanded and restructured, with new theorem on projective property of Lax pair in 3D
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1612.02753 Zobrazit plný text záznamu View this record from Arxiv