Related papers: Solutions of the hexagon equation for abelian anyo…
In this paper we consider the H\'enon problem in a ball. We prove the existence of (at least) one branch of nonradial solutions that bifurcate from the radial ones and that this branch is unbounded.
Conditions of the existence of solutions of linear and perturbed linear boundary value problems in the Hilbert spaces for the second order evolution equation are obtained.
In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…
We study a one-dimensional ordinary differential equation modelling optical conveyor belts, showing in particular cases of physical interest that periodic solutions exist. Moreover, under rather general assumptions it is proved that the set…
We give solutions to several decision problems in word hyperbolic groups
Over an algebraically closed field, we describe the affine varieties of solutions to the linear equations $a(xb)=c$ and $a(bx)=c$ over the split-octonions. We also determine the dimensions of the solution sets of arbitrary linear monomial…
A possibility to constrain axion-like particles from precision atomic physics is considered.
We discuss various methods and their effectiveness for solving linear equations over finitely generated abelian groups. More precisely, if $\varphi\colon G\to H$ is a homomorphism of finitely generated abelian groups and $b\in H$, we…
We study a class of initial boundary value problems of hyperbolic type. A new topological approach is applied to prove the existence of non-negative classical solutions. The arguments are based upon a recent theoretical result.
Exchanging particles on graphs, or more concretely on networks of quantum wires, has been proposed as a means to perform fault tolerant quantum computation. This was inspired by braiding of anyons in planar systems. However, exchanges on a…
We go on with the program started in the companion paper [CDI+] of defining a Poisson bracket structure on the space of solutions of the equations of motion of first order Hamiltonian field theories. The case of non-Abelian gauge theories…
We solve, by separation of variables, the problem of three anyons with a harmonic oscillator potential. The anyonic symmetry conditions from cyclic permutations are separable in our coordinates. The conditions from two-particle…
In this paper we study the complexity of solving orientable quadratic equations in wreath products $A\wr B$ of finitely generated abelian groups. We give a classification of cases (depending on genus and other characteristics of a given…
We consider properties of solitons in general orbifolds in the algebraic quantum field theory framework and constructions of solitons in affine and permutation orbifolds. Under general conditions we show that our construction gives all the…
The Hamilton-Jacobi equation for a Hamiltonian section on a Lie affgebroid is introduced and some examples are discussed.
The systematic method for the conversion of first class constraints to the equivalent set of Abelian one based on the Dirac equivalence transformation is developed. The representation for the corresponding matrix performing this…
A particular solution to the equations of motion of the Abelian Higgs model is given. The solution involves the Jacobi elliptic functions as well as the Heun functions.
We give several generalisations of the Deuring reduction criterion for elliptic curves to abelian varieties of higher dimension. In particular the Newton polygon of the reduction of an abelian variety A with complex multiplication by F at a…
A formulation of the Maxwell equations in terms of the split octonions is presented.
We study the existence of formal power series solutions to q-algebraic equations. When a solution exists, we give a sufficient condition on the equation for this solution to have a positive radius of convergence. We emphasize on the case…