$X$- and $Y$-invariants of Linear Partial Differential Operators in the plane (In Russian)

Details $X$- and $Y$-invariants of Linear Partial Differential Operators in the plane (In Russian) $X$- and $Y$-invariants of Linear Partial Differential Operators in the plane (In Russian)

2010-10-17

arxiv.org/abs/1010.3418v2

Programming and Computer Software, MAIK Nauka/Interperiodica, 192--196, Vol.37, issue 4, 2011

Mathematics

Analysis of PDEs

Scientific paper

10.1134/S0361768811020095

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.

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