We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s, t) and three arbitrary functions in t. Assuming analyticity of the arbitrary functions in a domain under consideration, we prove that the obtained solution is analytic and general. The Special Cosserat Theory of Rods describes the dynamic...

We extend our earlier work of revealing both space-space and space-time noncommuting structures in various models in particle mechanics exhibiting reparametrisation symmetry. We show explicitly (in contrast to the earlier results in our paper [8]) that for some special choices of the reparametrisation parameter ǫ, one can obtain space-space noncommuting structures which are Lie-algebraic in for...

Automorphic Lie Algebras are interesting because of their fundamental nature and their role in our understanding of symmetry. Particularly crucial is their description and classification as it allows us to understand and apply them in different contexts, from mathematics to physical sciences. While the problem of classification of Automorphic Lie Algebras with dihedral symmetry was already cons...

Continuous-time Markov chains are a standard tool in phylogenetic inference. If homogeneity is assumed, the chain is formulated by specifying time-independent rates of substitutions between states in the chain. In applications, there are usually extra constraints on the rates, depending on the situation. If a model is formulated in this way, it is possible to generalise it and allow for an inho...

We introduce the concept of algebra eigenstates which are defined for an arbitrary Lie group as eigenstates of elements of the corresponding complex Lie algebra. We show that this concept unifies different definitions of coherent states associated with a dynamical symmetry group. On the one hand, algebra eigenstates include different sets of Perelomov’s generalized coherent states. On the other...

In this paper, we study a generalized Zakharov–Kuznetsov equation in three variables, which has applications in the nonlinear development of ion-acoustic waves in a magnetized plasma. Conservation laws for this equation are constructed for the first time by using the new conservation theorem of Ibragimov. Furthermore, new exact solutions are obtained by employing the Lie symmetry method along w...

744 NOTICES OF THE AMS VOLUME 43, NUMBER 7 Introduction Mathematicians tend to think of the notion of symmetry as being virtually synonymous with the theory of groups and their actions, perhaps largely because of the well-known Erlanger program of F. Klein and the related work of S. Lie, which virtually defined geometric structures by their groups of automorphisms. (See, for example, Yaglom’s a...