%0 Journal Article
%T $X$- and $Y$-invariants of Linear Partial Differential Operators in the plane (In Russian)
%A Ekaterina Shemyakova
%J Mathematics
%D 2010
%I arXiv
%R 10.1134/S0361768811020095
%X We consider a classical problem of Computer Algebra: symbolic solution of PDEs. We transform the famous Darboux theorems on differential transformations of hyperbolic operator into the space of invariants. We introduce a new idea -- $X$- and $Y$-invariants of such operator as solutions of some equations written in terms of the Laplace invariants of this operator. Explicit formula for the changes in the sets of the $X$- and $Y$-invariants under the Darboux transformations are obtained.
%U http://arxiv.org/abs/1010.3418v2