39 citations · 76 across the 17 of their papers we have counts for
15 papers
Particle-like Structure of Lie algebras
Alexandre M. Vinogradov
If a Lie algebra structure g on a vector space is the sum of a family of mutually compatible Lie algebra structures g_i's, we say that g is simply assembled from the g_i's. Repeati…
Logic of differential calculus and the zoo of geometric strujctures
Alexandre M. Vinogradov
Since the discovery of differential calculus by Newton and Leibniz and the subsequent continuous growth of its applications to physics, mechanics, geometry, etc, it was observed th…
Some remarks on contact manifolds, Monge-Ampere equations and solution singularities
Alexandre Vinogradov
We describe some natural relations connecting contact geometry, classical Monge-Ampere equations and theory of singularities of solutions to nonlinear PDEs. They reveal the hidden…
What are symmetries of nonlinear PDEs and what are they themselves?
Alexandre M. Vinogradov
The general theory of (nonlinear) partial differential equations originated by S. Lie had a significant development in the past 30-40 years. Now this theory has solid foundations,…
Assembling Lie Algebras from Lieons
Alexandre M. Vinogradov
If a Lie algebra structures $\gG$ on a vector space is the sum of a family of mutually compatible Lie algebra structures $\gG_i$, we say that $\gG$ is \emph{simply assembled} from…
Scalar Differential Invariants of Symplectic Monge-Ampère Equations
Alessandro De Paris, Alexandre M. Vinogradov
All second order scalar differential invariants of symplectic hyperbolic and elliptic Monge-Ampère equations with respect to symplectomorphisms are explicitly computed. In particul…