Related papers: On the Ermakov systems and nonlocal symmetries

Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in…

We present noncommutative nonlinear supersymmetric theories. The first example is a non-polynomial Akulov-Volkov-type lagrangian with noncommutative nonlinear global supersymmetry in arbitrary space-time dimensions. The second example is…

In this paper we derive a general solution for the most general rotating and twisting locally rotationally symmetric spacetimes. This is achieved in three steps. First we decompose the manifold via 1+1+2 semi-tetrad formalism that yields a…

We explore the capacity of neural networks to detect a symmetry with complex local and non-local patterns : the gauge symmetry Z 2 . This symmetry is present in physical problems from topological transitions to QCD, and controls the…

Recent progress concerning regularization of supersymmetric theories is reviewed. Dimensional reduction is reformulated in a mathematically consistent way, and an elegant and general method is presented that allows to study the…

We address some conjectures and open problems in "analysis of symmetries" which include the study of non-commutative harmonic analysis and discontinuous groups for reductive homogeneous spaces beyond the classical framework: (1) discrete…

Characterizing the set of distributions that can be realized in the triangle network is a notoriously difficult problem. In this work, we investigate inner approximations of the set of local (classical) distributions of the triangle…

We develop efficient group-theoretical approach to the problem of classification of evolution equations that admit non-local transformation groups (quasi-local symmetries), i.e., groups involving integrals of the dependent variable. We…

It is well known that integrable hierarchies in (1+1) dimensions are local while the recursion operators that generate them usually contain nonlocal terms. We resolve this apparent discrepancy by providing simple and universal sufficient…

In this paper it is shown that Riemann invariants are invariant under nonclassical symmetries of a hyperbolic system. As a specific example, we study the one-dimensional shallow water equations on the flat and present another type…

In this work, we look at the symmetry of normal modes in symmetric structures, particularly structures with cyclic symmetry. We show that normal modes of symmetric structures have different levels of symmetry, or symmetricity. One novel…

Lie symmetry analysis is one of the powerful tools to analyze nonlinear ordinary differential equations. We review the effectiveness of this method in terms of various symmetries. We present the method of deriving Lie point symmetries,…

In this series of three articles, we give an exposition of various results and open problems in three areas of algebraic and geometric combinatorics: totally non-negative matrices, representations of the symmetric group, and hyperplane…

In this work, we study the Lie-point symmetries of Kepler--Ermakov systems presented by C. Athorne in J. Phys. A24 (1991), L1385--L1389. We determine the forms of arbitrary function H(x,y) in order to find the members of this class…

We start by introducing the basics of configurations of points and lines, and then move into discussing symmetry groups of these configurations. Specifically, we explore how we might classify the symmetries of $(9_3)$ and $(10_3)$ geometric…

In the last decade, it was understood that quantum networks involving several independent sources of entanglement which are distributed and measured by several parties allowed for completely novel forms of nonclassical quantum correlations,…

We show that the classification of the symmetric spaces can be achieved by K-theoretical methods. We focus on Hermitian symmetric spaces of non-compact type, and define K-theory for JB*-triples along the lines of C*-theory. K-groups have to…

Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…

Many quantum integrable systems are obtained using an accelerator physics technique known as Ermakov (or normalized variables) transformation. This technique was used to create classical nonlinear integrable lattices for accelerators and…

In this paper we review the known facts on isometries of Minkowski geometries and prove some new results on them. We give the normal forms of two special classes of operators and also characterize the isometry group of Minkowski $3$-spaces…