相关论文: Equivalence of Q-Conditional Symmetries under Grou…

New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate…

A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically…

We present classification of Q-conditional symmetries for the two-dimensional nonlinear wave equations and the reductions corresponding to these nonlinear symmetries. Classification of inequivalent reductions is discussed.

Symmetry groups of PDEs allow to transform solutions continuously into other solutions. In this paper, we use this property for the observability analysis of nonlinear PDEs with input and output. Based on a differential-geometric…

Potential equivalence transformations (PETs) are effectively applied to a class of nonlinear diffusion-convection equations. For this class all possible potential symmetries are classified and a theorem on connection of them with point ones…

We formulate the notion of quantum group symmetry of the Hamiltonian corresponding to Potts model and compute it for few simple models. Our examples illustrate how a slight change of the model parameter may result in a drastic change of the…

In terms of the analysis of fixed point subgroup and tensor decomposability of certain matrices, we study the equivalence of of quantum bipartite mixed states under local unitary transformations. For non-degenerate case an operational…

A Jet groupoid R_q over a manifold X is a special Lie groupoid consisting of q-jets of local diffeomorphisms from X to X. As a subbundle of the q-th order jet bundle of the trivial bundle X times X, a jet groupoid can be considered as a…

We establish two conditions equivalent to coamenability for type I locally compact quantum groups. The first condition is concerned with the spectra of certain convolution operators on the space…

A definition is given and the physical meaning of quantum transformations of a non-commutative configuration space (quantum group coactions) is discussed. It is shown that non-commutative coordinates which are transformed by quantum groups…

Using the theory of the symmetry group for PDEs [15, 17], we derive the symmetry group G associated to surfaces PDE. Several group invariant solutions of the surfaces PDE are given by solving a reduced system of partial differential…

A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity. The method involves an ansatz technique to solve an equivalent first-order PDE system of…

We present full classification of Q-conditional symmetries for the two-dimensional nonlinear wave equation.

We present a notion of symmetry for 1+1-dimensional integrable systems which is consistent with their group theoretic description and reproduces in special cases the known Baecklund transformation for the generalized Korteweg-deVries…

The nonlocal properties of arbitrary dimensional bipartite quantum systems are investigated. A complete set of invariants under local unitary transformations is presented. These invariants give rise to both sufficient and necessary…

We consider the problem of performing the preliminary "symmetry classification'' of a class of quasi-linear PDE's containing one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial…

It is known that local operators in quantum field theory transform in representations of ordinary global symmetry groups. The purpose of this paper is to generalise this statement to extended operators such as line and surface defects. We…

We study quantum field theories which have quantum groups as global internal symmetries. We show that in such theories operators are generically non-local, and should be thought as living at the ends of topological lines. We describe the…

We construct a relativistically covariant symmetry of QED. Previous local and nonlocal symmetries are special cases. This generalized symmetry need not be nilpotent, but nilpotency can be arranged with an auxiliary field and a certain…

This short note completes the symmetry analysis of a class of quasi-linear partial differential equations considered in the previous paper (Nonlinear Dynamics, Vol. 51, 309-316 (2008)): it deals with the presence of an "exceptional" Lie…