The problem of finding Lie point symmetries for a certain class multi-dimensional nonlinear partial fractional differential equations and their systems is studied. It assumed that considered involve derivatives with respect to only one independent variable, each equation contains single derivative. most significant examples such are time-fractional models processes memory power-law type. Two di...

We generalize Cartan's logarithmic derivative of a smooth map from manifold into Lie group $G$ to maps homogeneous space $M=G/H$, and determine the global monodromy obstruction reconstructing such infinitesimal data. The embedding submanifold $\Sigma \subset M$ becomes an invariant $ under symmetries "Klein geometry" $M$ whose analysis is taken up in [SIGMA 14 (2018), 062, 36 pages, arXiv:1703....

A passive orthonomic system of PDEs defines a submanifold in the corresponding jet manifold, coordinated by so called parametric derivatives. We restrict the total differential operators and the prolongation of an evolutionary vector field v to this submanifold. We show that the vanishing of their commutators is equivalent to v being a generalized symmetry of the system. 1 The standard symmetry...

We establish a link between the CR geometry of real analytic submanifolds in I C and the geometric PDE theory. The main idea of our approach is to consider biholomorphisms of a Levi-nondegenerate real analytic Cauchy-Riemann manifold M as poinwise symmetries of a second order holomorphic PDE system defining the Segre family of M. This allows to employ the well-elaborated PDE tools in order to s...

We define a natural generalized symmetry of the Yang-Mills equations as an infinitesimal transformation of the Yang-Mills field, built in a local, gauge invariant, and Poincaré invariant fashion from the Yang-Mills field strength and its derivatives to any order, which maps solutions of the field equations to other solutions. On the jet bundle of Yang-Mills connections we introduce a spinorial ...

We study the group properties and similarity solutions for constraint conditions of anti-self-dual null K\"{a}hler four-dimensional manifolds with at least a Killing symmetry vector. Specifically we apply theory Lie symmetries to determine all infinitesimal generators one-parameter point transformations which leave system invariant. use these define invariant are used simplify differential equa...

The Noether symmetry of a generic f(R) cosmological model is investigated by utilizing the behavior of the corresponding Lagrangian under the infinitesimal generators of the desired symmetry. We explicitly calculate the form of f(R) for which such symmetries exist. It is shown that the resulting form of f(R) yields a power law expansion for the cosmological scale factor. We also obtain the effe...

The infinitesimal symmetries of a fully decomposed non-Abelian gerbe can be generated in terms of a nilpotent BRST operator, which is here constructed. The appearing fields find a natural interpretation in terms of the universal gerbe, a generalisation of the universal bundle. We comment on the construction of observables in the arising Topological Quantum Field Theory. It is also shown how the...

The hierarchy of the integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of the linearization of these equations and their conservation law in the terms of the solutions of the corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of the lineari...