In the recent B̂ılă’s paper [1] it was determined the symmetry group of the minimal surfaces PDE (using classical methods). The aim of this paper is to find the Lie algebra of contact symmetries of the minimal surfaces PDE using the correspondence, established by V. V. Lychagin [2], between the second order non-linear differential operators and differential forms which are given on the manifold ...

The Darboux theory of integrability for planar polynomial differential equations is a classical field, with connections to Lie symmetries, differential algebra and other areas of mathematics. In the present paper we introduce the concepts, problems and inverse problems, and we outline some recent results on inverse problems. We also prove a new result, viz. a general finiteness theorem for the ...

We show that the tree-level part of a theory of finite type invariants of 3-manifolds (based on surgery on objects called claspers, Y-graphs or clovers) is essentially given by classical algebraic topology in terms of the Johnson homomorphism and Massey products, for arbitrary 3-manifolds. A key role of our proof is played by the notion of a homology cylinder, viewed as an enlargement of the ma...

We study a Lagrangian extension of the 5d Martínez Alonso–Shabat equation \(\mathcal {E}\)$$\begin{aligned} u_{yz}=u_{tx}+u_y\,u_{xs}-u_x\,u_{ys} \end{aligned}$$that coincides with cotangent {T}^{*}\mathcal {E}\) to latter. describe Lie algebra structure its symmetries (which happens be quite nontrivial and is described in terms deformations) construct two families recursion operators for symme...

The derivation d T on the exterior algebra of forms on a manifold M with values in the exterior algebra of forms on the tangent bundle T M is extended to multivector fields. These tangent lifts are studied with applications to the theory of Poisson structures, their symplectic foliations, canonical vector fields and Poisson-Lie groups. 0. Introduction. A derivation d T on the exterior algebra o...

The Cartan group is the free nilpotent Lie of rank 2 and step 3. We consider left-invariant sub-Riemannian problem on defined by an inner product in first layer its algebra. This gives a approximation arbitrary with growth vector (2,3,5). In previous works, we described symmetries group, corresponding Maxwell time — when symmetric geodesics intersect one another. It known that are not globally ...

Abstract Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions linearisation (Frechet derivative) holding on space to PDE, and they are well-known comprise linear having structure Lie algebra. Solutions adjoint PDE called adjoint-symmetries. Their algebraic for general systems is studied herein. This motivated by correspondence between v...

Previous results on quasi-classical limit of the KP and Toda hierarchies are now extended to the BKP hierarchy. Basic tools such as the Lax representation, the Baker-Akhiezer function and the tau function are reformulated so as to fit into the analysis of quasi-classical limit. Two subalgebras WB 1+∞ and w B 1+∞ of the Winfinity algebrasW1+∞ and w1+∞ are introduced as fundamental Lie algebras o...

• Constant Coriolis parameter can be cancelled in the primitive equations. The cancellation is realized by a point transformation. transformation constructed algebraic method. complete symmetry group of equations computed. Modern weather and climate prediction models are based on system nonlinear partial differential called Lie symmetries with zero external heating rate computed structure its m...

In this work, we revisit several families of standard Hamiltonians that appear in the literature and discuss their symmetries conserved quantities language commutant algebras. particular, start with defined by parts are local, study algebra operators separately commute each part. The models include spin-1/2 Heisenberg model its deformations, types spinless spinful free-fermion models, Hubbard m...