Konopelchenko B G, Schief W K
Department of Mathematics and Physics, University of Salento and INFN, Sezione di Lecce, 73100 Lecce, Italy.
School of Mathematics and Statistics, The University of New South Wales, Sydney, New South Wales 2052, Australia.
Proc Math Phys Eng Sci. 2019 Oct;475(2230):20190091. doi: 10.1098/rspa.2019.0091. Epub 2019 Oct 16.
Based on the commutativity of scalar vector fields, an algebraic scheme is developed which leads to a privileged multi-dimensionally consistent 2 + 2-dimensional integrable partial differential equation with the associated eigenfunction constituting an infinitesimal symmetry. The 'universal' character of this novel equation of vanishing Pfaffian type is demonstrated by retrieving and generalizing to higher dimensions a great variety of well-known integrable equations such as the dispersionless Kadomtsev-Petviashvili and Hirota equations and various avatars of the heavenly equation governing self-dual Einstein spaces.
基于标量向量场的可交换性，开发了一种代数方案，该方案导致一个具有特权的多维一致的2 + 2维可积偏微分方程，其相关的本征函数构成一个无穷小对称性。通过检索并推广到更高维度的各种著名可积方程，如无色散Kadomtsev-Petviashvili方程和Hirota方程以及控制自对偶爱因斯坦空间的天国方程的各种变体，证明了这种新型Pfaffian消失型方程的“通用”特征。
