论文标题
与Liouville类型双曲线方程相关的Hamiltonian前操作员
Pre-Hamiltonian operators related to hyperbolic equations of Liouville type
论文作者
论文摘要
该文本专门用于双曲程方程，该方程允许差异操作员将一个自变量的任何函数映射到相应方程的对称性中。我们为此类操作员使用术语“对称驱动程序”，并证明最小订单的任何对称驱动程序是hamiltonian（即，驱动程序的图像相对于标准支架都关闭）。这使我们能够证明，如果对称驱动程序和积分都具有最小的订单，则对称驱动器与积分的Fréchet衍生物的组成也是hamiltonian（在新的变量集中）。
This text is devoted to hyperbolic equations admitting differential operators that map any function of one independent variable into a symmetry of the corresponding equation. We use the term `symmetry driver' for such operators and prove that any symmetry driver of the smallest order is pre-Hamiltonian (i.e., the image of the driver is closed with respect to the standard bracket). This allows us to prove that the composition of a symmetry driver with the Fréchet derivative of an integral is also pre-Hamiltonian (in a new set of the variables) if both the symmetry driver and the integral have the smallest orders.
