We study the equation Efc of flat connections in a given fiber bundle and discover a specific geometric structure on it, which we call a flat representation. We generalize this notion to arbitrary PDE and prove that flat representations of an equation E are in 1-1 correspondence with morphisms φ : E → Efc, where E and Efc are treated as submanifolds of infinite jet spaces. We show that flat rep...

Symmetries are ubiquitous in nature. Almost all organisms have some kind of “symmetry”, meaning that their shape does not change under geometric transformation. This geometrical concept symmetry is intuitive and easy to recognize. On the other hand, behavior many biological systems over time can be described with ordinary differential equations. These dynamic models may also possess “symmetries...

Symmetry is one of the most important properties of a shape, unifying form and function. It encodes semantic information on one hand, and affects the shape’s aesthetic value on the other. Symmetry comes in many flavors, amongst the most interesting being intrinsic symmetry, which is defined only in terms of the intrinsic geometry of the shape. Continuous intrinsic symmetries can be represented ...

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

This article provides us with a unifying classification of the conformal infinitesimal symmetries of non-relativistic Newton-Cartan spacetime. The Lie algebras of non-relativistic conformal transformations are introduced via the Galilei structure. They form a family of infinite-dimensional Lie algebras labeled by a rational “dynamical exponent”, z. The Schrödinger-Virasoro algebra of Henkel et ...

In this paper the programs APPLYSYM, QUASILINPDE and DETRAFO are described which aim at the utilization of infinitesimal symmetries of differential equations. The purpose of QUASILINPDE is the general solution of quasilinear PDEs. This procedure is used by APPLYSYM for the application of point symmetries for either • calculating similarity variables to perform a point transformation which lower...

It is shown that the Ginsparg-Wilson relation implies an exact symmetry of the fermion action, which may be regarded as a lattice form of an infinitesimal chiral rotation. Using this result it is straightforward to construct lattice Yukawa models with unbroken flavour and chiral symmetries and no doubling of the fermion spectrum. A contradiction with the Nielsen-Ninomiya theorem is avoided, bec...

Using a formalism of minitwistors, we derive infinitely many conserved charges for the sl(∞)-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions. E-mail address; be10@dk...

Abstract The Lie symmetry analysis is adopted to the (2 + 1)-dimensional dispersionless B-type Kadomtsev–Petviashvili (dBKP) equation. combination of and symbolic computing methods proves that algebra infinitesimal dBKP equation depends on four independent arbitrary functions one parameter. reduced classes for deriving commutative relations, group invariant solutions conservation laws, optimal ...