论文标题
关于Monge-ampère方程和Monge-Ampère系统的概括
On a generalization of Monge-Ampère equations and Monge-Ampère systems
论文作者
论文摘要
我们从差异几何学的角度讨论Monge-ampère方程。众所周知，Monge-ampère方程对应于1射流空间上的特殊外部差分系统。在本文中，我们概括了Monge-ampère方程式，并证明了$（k+1）$ streser Permorized Monge-ampère方程对应于$ K $ -JET空间上的特殊外部差速器系统。然后，其解决方案自然对应于相应的外部微分系统的积分歧管。此外，我们验证了Korteweg-de Vries（KDV）方程和Cauchy-Riemann方程是我们方程式的示例。
We discuss Monge-Ampère equations from the view point of differential geometry. It is known that a Monge-Ampère equation corresponds to a special exterior differential system on a 1-jet space. In this paper, we generalize Monge-Ampère equations and prove that a $(k+1)$st order generalized Monge-Ampère equation corresponds to a special exterior differential system on a $k$-jet space. Then its solution naturally corresponds to an integral manifold of the corresponding exterior differential system. Moreover, we verify that the Korteweg-de Vries (KdV) equation and the Cauchy-Riemann equations are examples of our equation.
