We describe three ways of modifying the relativistic Heisenberg algebra first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of generalized deformed phase space with the semidirect product of two dual Hopf algebras describing quantum group of motions and the corresponding quantum Lie algebra. As...

In this paper, we consider a generalized BenjaminBona-Mahony-Burgers equation. Classical symmetries of this equation are considered. The functional forms, for which the BBMB equation can be reduced to ordinary differential equations by classical Lie symmetries, are obtained. A catalogue of symmetry reductions and a catalogue of exact solutions are given. A set of new solitons, kinks, antikinks,...

We describe three ways of modifying the relativistic Heisenberg algebra-first one not linked with quantum symmetries, second and third related with the formalism of quantum groups. The third way is based on the identification of generalized deformed phase space with the semidirect product of two dual Hopf algebras describing quantum group of motions and the corresponding quantum Lie algebra. As...

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 introduced to reduce theories on an infinite lattice to those on semi-infinite, or finite ones.

A bstract We study reductions of 6d theories on a d -dimensional manifold M , focusing the interplay between symmetries, anomalies, and dynamics resulting (6 ? )-dimensional theory T [ ]. refine generalize notion “polarization” to polarization which serves fix spectrum local extended operators in Another important feature ] is that they often possess higher-group such as 2-group 3-group symmetr...