13 citations · 36 across the 9 of their papers we have counts for
12 papers
Singularities in one-dimensional Euler flows
Mikhail Roop
In this paper, a system of one-dimensional gas dynamics equations is considered. This system is a particular case of Jacobi type systems and has a natural representation in terms o…
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…
Singularities in Euler flows: multivalued solutions, shock waves, and phase transitions
Valentin Lychagin, Mikhail Roop
In this paper, we analyze various types of critical phenomena in one-dimensional gas flows described by Euler equations. We give a geometrical interpretation of thermodynamics with…
On Higher Order Structures in Thermodynamics
Valentin Lychagin, Mikhail Roop
We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of e…
Shock Waves in Euler Flows of Gases
Valentin Lychagin, Mikhail Roop
Non-stationary Euler flows of gases are studied. The system of differential equations describing such flows can be represented by means of 2-forms on zero-jet space and we get some…
Schrödinger equations on elliptic curves: symmetries, solutions and eigenvalue problem
Valentin Lychagin, Mikhail Roop
In this paper, we study Schrödinger equations on elliptic curves called generalized Lamé equations. We suggest a method of finding integrable potentials for Schrödinger type equati…