Name: Ekaterina Shemyakova
Academic Rank: Assistant Professor
Expertise Keywords: Darboux transformations, exact solutions of PDEs, factorization, Integrable systems, Laplace transformations, Lax pairs, Linear Partial Differential Operators
Available For: interviews, essays, speaking
Currrent Research: Partial Differential Equations (integrable systems),
Positions held prior to joining SUNY New Paltz:
Postdoctoral fellow, University of Western Ontario, Canada
Postdoctoral fellow, Research Institute for Symbolic Computation, Austria
|Research Institute for Symbolic Computation, Austria||2004-2007||PhD||2007||Math|
|Moscow State University||1999-2004||M.Sc. and B.Sc.||2004||Math|
Factorization of Darboux Transformations of Arbitrary Order for Two-dimensional Schroedinger operator, 2014 (submitted).
Invertible Darboux Transformations , Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 9, 002, 2013.
Invariants for Darboux transformations of Arbitrary Order for DxDy+aDx+bDy+c , Geometric Methods in Physics, 2013.
Proof of the Completeness of Darboux Wronskian Formulae for Order Two, Canadian Journal of Mathematics, 65, no. 3, 2013.
Package LPDO for MAPLE, Programming and Computer Software, no. 2, 2013.
Laplace Transformations as the Only Degenerate Darboux Transformations of First Order, Programming and Computer Software, v. 38, no. 2, 2012.
X- and Y-invariants of partial differential operators in the plane , Programming and Computer Software, (37), no.4, pp.192-196, 2011.
Book chapter: with F. Winkler, Linear Partial Differential Equations and Linear Partial Differential Operators in Computer Algebra, in Monographs in Symbolic Computation, Springer,
editors: P. Paule et al., vol. Progress and Prospects in Numerical and Symbolic Scientific Computing, 2011.
Refinement of Two-Factor Factorizations of a Linear Partial Differential Operator of Arbitrary Order and Dimension, Mathematics in Computer Science, (4), no.2-3, pp. 223-230, 2010.
(with S.I.Khashin, and D.J.Jeffrey), Conjecture concerning a completely monotonic function, Computers & Mathematics with Applications, vol. 60, issue 5, pp.1360-1363, 2010.
Multiple factorizations of bivariate linear partial differential operators, Lecture Notes in Computer Science, vol. 5743, pp. 299--309, 2009.
On the invariant properties of non-hyperbolic third-order linear partial differential operators, Conferences on Intelligent Computer Mathematics, vol.5625, pp.154--169, 2009.
(with S.Tsarev) Differential transformations of parabolic second-order operators in the plane, Proceedings Steklov Inst. Math. (Moscow), vol.266, pp.219--227, 2009.
(with E.Mansfield), Moving frames for Laplace invariants, Proceedings of ISSAC 2008 (The International Symposium on Symbolic and Algebraic Computation), pp.295--302, 2008.
(with F.Winkler), On the invariant properties of hyperbolic bivariate third-order linear partial differential operators, Lecture Notes in Artificial Intelligence, vol.5081, pp.199--212, 2007.
(with F.Winkler), A full system of invariants for third-order linear partial differential operators in general form, Lecture Notes in Comput. Sci., vol.4770, pp.360--369, 2007.
The Parametric Factorizations of Second-, Third- and Fourth-Order Linear Partial Differential Operators on the Plane , Mathematics in Computer Science, vol.1, no.2, pp.225--237, 2007.
(with F.Winkler), Obstacles to the Factorization of Linear Partial Differential Operators into Several Factors , Programming and Computer Software, vol.33, no.2, pp.67--73, 2007.
(with F.Winkler), Symbolic and Algebraic Methods for Linear Partial Differential Operators , Lecture Notes in Computer Science, vol.4770, 2007.
(with F.Winkler), Obstacle to Factorization of LPDOs, in Proc. Transgressive Computing 2006 (J.-G. Dumas, ed.), pp.435--441, 2006.
A full system of invariants for third-order linear partial differential operators, Lecture Notes in Computer Science, vol.4120, pp.360--369, 2006.
Involutive divisions. Graphs., Programming and Computer Software, vol.30, no.2, pp.68--74, 2004.
Involutive divisions for effective involutive algorithms, Fundam. Prikl. Mat., vol.9, no.3, pp.237--253, 2003.