Jordan manifolds and dispersionless KdV equations
Exactly Solvable and Integrable Systems
2017-02-08 v1
Abstract
Multicomponent KdV-systems are defined in terms of a set of structure constants and, as shown by Svinolupov, if these define a Jordan algebra the corresponding equations may be said to be integrable, at least in the sense of having higher-order symmetries, recursion operators and hierarchies of conservation laws. In this paper the dispersionless limits of these Jordan KdV equations are studied, under the assumptions that the Jordan algebra has a unity element and a compatible non-degenerate inner product. Much of this structure may be encoded in a so-called Jordan manifold, akin to a Frobenius manifold. In particular the Hamiltonian properties of these systems are investigated.
Cite
@article{arxiv.nlin/0010058,
title = {Jordan manifolds and dispersionless KdV equations},
author = {Ian A. B. Strachan},
journal= {arXiv preprint arXiv:nlin/0010058},
year = {2017}
}