On classification and invariants of second order non-parabolic linear partial differential equations in two variables

摘要: The paper deals with second order abstract linear partial differential equations (LPDE) over a field two commuting operators. In terms of usual the main content can be presented as follows. classification and invariants problems for LPDEs respect to transformations \[x=x(\xi,\eta),\ y=y(\xi,\eta),\ u=h(x,y)v(\xi,\eta),\] where $x,y$ are independent $u$ is dependent variable LPDE, considered. Solutions these given different subclasses non-parabolic LPDE which appear naturally in equivalence problem LPDE. A criterion reducibility such constant coefficients offered well.