Involution and Symmetry Reductions
نویسنده
چکیده
After reviewing some notions of the formal theory of diierential equations we discuss the completion of a given system to an involutive one. As applications to symmetry theory we study the eeects of local solvability and of gauge symmetries, respectively. We consider non-classical symmetry reductions and more general reductions using diierential constraints.
منابع مشابه
Lie symmetry analysis for Kawahara-KdV equations
We introduce a new solution for Kawahara-KdV equations. The Lie group analysis is used to carry out the integration of this equations. The similarity reductions and exact solutions are obtained based on the optimal system method.
متن کاملUltra and Involution Ideals in $BCK$-algebras
In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...
متن کاملInvolution Matrices of Real Quaternions
An involution or anti-involution is a self-inverse linear mapping. In this paper, we will present two real quaternion matrices, one corresponding to a real quaternion involution and one corresponding to a real quaternion anti-involution. Moreover, properties and geometrical meanings of these matrices will be given as reflections in R^3.
متن کاملSesquilinear forms over rings with involution
Many classical results concerning quadratic forms have been extended to Hermitian forms over algebras with involution. However, not much is known in the case of sesquilinear formswithout any symmetry property. The present paperwill establish aWitt cancellation result, an analogue of Springer’s theorem, as well as some local–global and finiteness results in this context. © 2013 Elsevier B.V. All...
متن کاملMinimal Bounded Lattices with an Antitone Involution the Complemented Elements of Which Do Not Form a Sublattice
Bounded lattices with an antitone involution the complemented elements of which do not form a sublattice must contain two complemented elements such that not both their join and their meet are complemented. We distinguish (up to symmetry) eight cases and in each of these cases we present such a lattice of minimal cardinality.
متن کامل