A Geometry for Multidimensional Integrable Systems
高能物理 - 理论
2020-12-16 v1 可精确求解与可积系统
solv-int
摘要
A deformed differential calculus is developed based on an associative star-product. In two dimensions the Hamiltonian vector fields model the algebra of pseudo-differential operator, as used in the theory of integrable systems. Thus one obtains a geometric description of the operators. A dual theory is also possible, based on a deformation of differential forms. This calculus is applied to a number of multidimensional integrable systems, such as the KP hierarchy, thus obtaining a geometrical description of these systems. The limit in which the deformation disappears corresponds to taking the dispersionless limit in these hierarchies.
引用
@article{arxiv.hep-th/9604142,
title = {A Geometry for Multidimensional Integrable Systems},
author = {I. A. B. Strachan},
journal= {arXiv preprint arXiv:hep-th/9604142},
year = {2020}
}
备注
LaTeX, 29 pages. To be published in J.Geom.Phys