辛蒙日-安培方程的标量微分不变式
Scalar Differential Invariants of Symplectic Monge-Ampère Equations
摘要：
显式计算了辛双曲和椭圆蒙日-安培方程关于辛同胚的所有二阶标量微分不变式.特别是，它表明，独立的二阶不变量的数量等于7，在一般的蒙日-安培方程，这个数字等于2形成鲜明对比。我们还介绍了一系列的不变微分形式和向量场，使我们能够构建许多高阶的标量微分不变式。引入的不变量给出了蒙日-安培方程的辛等价解。作为一个例子，我们研究拟线性方程的一种合适的，特别是找到一个简单的线性化准则。
英文摘要：
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particular, it is shown that the number of independent second order invariants is equal to 7, in sharp contrast with general Monge-Ampère equations for which this number is equal to 2. We also introduce a series of invariant differential forms and vector fields which allows us to construct numerous scalar differential invariants of higher order. The introduced invariants give a solution of the symplectic equivalence of Monge-Ampère equations. As an example we study quasilinear equations of a suitable kind and in particular find a simple linearization criterion.
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