20 citations · 84 across the 22 of their papers we have counts for
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Proof of the Completeness of Darboux Wronskian Formulae for Order Two
Ekaterina Shemyakova
Darboux Wronskian formulas allow to construct Darboux transformations, but Laplace transformations, which are Darboux transformations of order one cannot be represented this way. I…
Multiple Factorizations of Bivariate Linear Partial Differential Operators
Ekaterina Shemyakova
We study the case when a bivariate Linear Partial Differential Operator (LPDO) of orders three or four has several different factorizations. We prove that a third-order bivariate L…
Parametric Factorizations of Second-, Third- and Fourth-Order Linear Partial Differential Operators with a Completely Factorable Symbol on the Plane
Ekaterina Shemyakova
Parametric factorizations of linear partial operators on the plane are considered for operators of orders two, three and four. The operators are assumed to have a completely factor…
Obstacles to the Factorization of Linear Partial Differential Operators into Several Factors
Ekaterina Shemyakova, Franz Winkler
We consider algorithms for the factorization of linear partial differential operators. We introduce several new theoretical notions in order to simplify such considerations. We def…
- and -invariants of Linear Partial Differential Operators in the plane (In Russian)
Ekaterina Shemyakova
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…
Refinement of Two-Factor Factorizations of a Linear Partial Differential Operator of Arbitrary Order and Dimension
Ekaterina Shemyakova
Given a right factor and a left factor of a Linear Partial Differential Operator (LPDO), under which conditions we can refine these two-factor factorizations into one three-factor…