Related papers: On the geometry of lambda-symmetries, and PDEs red…
We investigate geometric properties of homogeneous parabolic geometries with generalized symmetries. We show that they can be reduced to a simpler geometric structures and interpret them explicitly. For specific types of parabolic…
We consider the theory of \emph{twisted symmetries} of differential equations, in particular $\lambda$ and $\mu$-symmetries, and discuss their geometrical content. We focus on their interpretation in terms of gauge transformations on the…
We introduce and study a new class of $\eps$-convex bodies (extending the class of convex bodies) in metric and normed linear spaces. We analyze relations between characteristic properties of convex bodies, demonstrate how $\eps$-convex…
An alternative proof of Lie's approach for linearization of scalar second order ODEs is derived using the relationship between $\lambda$-symmetries and first integrals. This relation further leads to a new $\lambda$-symmetry linearization…
This paper describes the notion of \sigma -symmetry, which extends the one of \lambda-symmetry, and its application to reduction procedures of systems of ordinary differential equations and of dynamical systems as well. We also consider…
We observe that, up to conjugation, a majority of symmetric higher order ODEs (ordinary differential equations) and ODE systems have only fiber-preserving point symmetries. By exploiting Lie's classification of Lie algebras of vector…
It is known that many equations of interest in Mathematical Physics display solutions which are only asymptotically invariant under transformations (e.g. scaling and/or translations) which are not symmetries of the considered equation. In…
In this present paper, we study geometric structures of rank two prolongations of implicit second-order partial differential equations (PDEs) for two independent and one dependent variables and characterize the type of these PDEs by the…
The Lie symmetries of a large class of generalized Toda field theories are studied and used to perform symmetry reduction. Reductions lead to generalized Toda lattices on one hand, to periodic systems on the other. Boundary conditions are…
We study the Lie point symmetries of a general class of partial differential equations (PDE) of second order. An equation from this class naturally defines a second-order symmetric tensor (metric). In the case the PDE is linear on the first…
For the class of systems of PDEs, for which infinitesimal translations (with respect to some (in)dependent variables) possess specific finite-dimensional invariant subspaces of the space of generalized symmetries of the system considered.…
We investigate metric projections and distance functions referring to convex bodies in finite-dimensional normed spaces. For this purpose we identify the vector space with its dual space by using, instead of the usual identification via the…
This expository monograph cuts a short path from the common, elementary background in geometry (linear algebra, vector bundles, and algebraic ideals) to the most advanced theorems about involutive exterior differential systems: (1) The…
We embed the geometries of the generalized $\lambda$-deformations into the framework of the Double Field Theory.
In this paper we describe the geometry of distributions by their symmetries, and present a simplified proof of the Frobenius theorem and some related corollaries. Then, we study the geometry of solutions of $F-$Gordon equation; A PDE which…
We consider the linear space of composite fields as an infinite dimensional vector bundle over the theory space whose coordinates are simply the parameters of a renormalized field theory. We discuss a geometrical expression for the short…
We discuss various compatibility criteria for overdetermined systems of PDEs generalizing the approach to formal integrability via brackets of differential operators. Then we give sufficient conditions that guarantee that a PDE possessing a…
Partial differential equations (PDEs) are among the most universal and parsimonious descriptions of natural physical laws, capturing a rich variety of phenomenology and multi-scale physics in a compact and symbolic representation. This…
The paper proved that every $C^2$-solution of a given first order PDEs system, regarded on the jet fibre bundle of order one $J^1(T,M)$, may be viewed as a "generalized harmonic map", via the least squares variational method. Our ideas are…
We consider a generalisation of vector fields on a vector space, where the vector space is generalised to a highest-weight module over a Kac-Moody algebra. The generalised vector field is an element in a non-associative superalgebra defined…