25 citations · 119 across the 42 of their papers we have counts for
51 papers
On invariants and equivalence of differential operators under Lie pseudogroups actions
Valentin Lychagin, Valeriy Yumaguzhin
In this paper, we study invariants of linear differential operators with respect to algebraic Lie pseudogroups. Then we use these invariants and the principle of n-invariants to ge…
On natural invariants and equivalence of differential operators
Valentin Lychagin, Valeriy Yumaguzhin
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of order on a smooth manifold of dimension $…
Natural differential invariants and equivalence of third order nonlinear differential operators
Valentin Lychagin, Valeriy Yumaguzhin
We give a description of the field of rational natural differential invariants for a class of nonlinear differential operators of the third order on a two dimensional manifold and…
Quotient of the Euler system on one class of curves
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
We consider the Euler system describing a one-dimensional inviscid flows in space along curves of a certain class. Using differential invariants for the Euler system, we obtain its…
Quotients of Navier--Stokes equation on space curves
Anna Duyunova, Valentin Lychagin, Sergey Tychkov
A Navier--Stokes system on a curve is discussed. The quotient equation for this system is found. The quotient is used to find some solutions of Navier--Stokes system. Using virial…
Differential Invariants in Algebra
Valentin Lychagin, Mikhail Roop
In these lectures, we discuss two approaches to studying orbit spaces of algebraic Lie groups. Due to algebraic approach orbit space, or quotient, is an algebraic manifold, while f…