4D 可积无色散偏微分方程、其对称伪群与形变
数学物理
2015-10-28 v2 微分几何
math.MP
摘要
我们研究了 4D 中 Hirota 类型的可积非退化 Monge-Ampère 方程，并证明其对称代数具有独特的分级结构，从而唯一确定了这些方程。利用这一性质，我们将这类 heavenly 型方程形变为具有大对称伪群的新一类二阶可积偏微分方程。我们对所获得的对称形变进行了分类，并讨论了其解的自对偶超 Hermitian 几何，该几何通过 twistor 理论编码了可积性。
引用
@article{arxiv.1410.7104,
title = {Integrable dispersionless PDE in 4D, their symmetry pseudogroups and deformations},
author = {Boris Kruglikov and Oleg Morozov},
journal= {arXiv preprint arXiv:1410.7104},
year = {2015}
}
备注
This version is updated with an appendix about multi-component extensions of the integrable equations. Our deformations can be considered as reductions of such extensions (as they are reductions of the self-duality equation), but we stress that second order deformations carry the natural geometry which encodes integrability. We also expanded the introduction a bit