34 citations · 96 across the 19 of their papers we have counts for
8 papers · 1 filter
On weakly commutative triples of partial differential operators
Sergey P. Tsarev, Vitaly A. Stepanenko
We investigate algebraic properties of weakly commutative triples, appearing in the theory of integrable nonlinear partial differential equations. Algebraic technique of skew field…
On Local Description of Two-Dimensional Geodesic Flows with a Polynomial First Integral
Maxim V. Pavlov, Sergey P. Tsarev
In this paper we construct multiparametric families of two dimensional metrics with polynomial first integral. Such integrable geodesic flows are described by solutions of some sem…
Classical Mechanical Systems with one-and-a-half Degrees of Freedom and Vlasov Kinetic Equation
Maxim V. Pavlov, Sergey P. Tsarev
We consider non-stationary dynamical systems with one-and-a-half degrees of freedom. We are interested in algorithmic construction of rich classes of Hamilton's equations with the…
Hyperdeterminants as integrable discrete systems
Sergey P. Tsarev, Thomas Wolf
We give the basic definitions and some theoretical results about hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability (understood as 4d-consistency) of a nonl…
Second order quasilinear PDEs and conformal structures in projective space
P. A. Burovskiy, E. V. Ferapontov, S. P. Tsarev
We investigate second order quasilinear equations of the form f_{ij} u_{x_ix_j}=0 where u is a function of n independent variables x_1, ..., x_n, and the coefficients f_{ij} are fu…
Classification of 3-dimensional integrable scalar discrete equations
S. P. Tsarev, T. Wolf
We classify all integrable 3-dimensional scalar discrete quasilinear equations Q=0 on an elementary cubic cell of the 3-dimensional lattice. An equation Q=0 is called integrable if…