Related papers: Supersymmetry, shape invariance and the Legendre e…

We prove the global in time existence of spherically symmetric solutions to an initial-boundary value problem for a system of partial differential equations, which consists of the equations of linear elasticity and a nonlinear,…

We use a modification of the parameterization method to study invariant manifolds for difference equations. We establish existence, regularity, smooth dependence on parameters and study several singular limits, even if the difference…

There are a number of publications on relativistic objects dealing either with black holes or naked singularities in the center. Here we show that there exist static spherically symmetric solutions of Einstein equations with a strongly…

The N-dimensional generalization of Bertrand spaces as families of Maximally superintegrable systems on spaces with nonconstant curvature is analyzed. Considering the classification of two dimensional radial systems admitting 3 constants of…

How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical…

It is well known that the real and imaginary parts of any holomorphic function are harmonic functions of two variables. In this paper we generalize this property to finite-dimensional commutative algebras. We prove that if some basis of a…

We consider some nonlinear elliptic equations on ${\mathbb R}^n$ and ${\mathbb S}^n$. By the method of moving spheres, we obtain the symmetry properties of solutions and some nonexistence results. Moreover, by the global bifurcation theory,…

The automorphism invariant theory of Crawford[J. Math. Phys. 35, 2701 (1994)] has show great promise, however its application is limited by the paradigm to the domain of spin space. Our conjecture is that there is a broader principle at…

Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent lengthscale, or coarsening (increase of the lengthscale with time) are the two major alternatives. When and under which conditions one…

Coupled wave equations are popular tool for investigating longitudinal dynamical effects in semiconductor lasers, for example, sensitivity to delayed optical feedback. We study a model that consists of a hyperbolic linear system of partial…

Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…

We investigate relativistic spherically symmetric static perfect fluid models in the framework of the theory of dynamical systems. The field equations are recast into a regular dynamical system on a 3-dimensional compact state space,…

This article reviews the role of hidden symmetries of dynamics in the study of physical systems, from the basic concepts of symmetries in phase space to the forefront of current research. Such symmetries emerge naturally in the description…

An integrable hierarchies connected with linear stationary Schr\"odinger equation with energy dependent potentials (in general case) are considered. Galilei-like and scaling invariance transformations are constructed. A symmetry method is…

In this article we establish the radial symmetry of positive solutions of a p- Laplace equation in the Hyperbolic space, which is the Euler Lagrange equation of the p- Poincare Sobolev inequality in the Hyperbolic space. We will also…

The supersymmetry of the electron in both the nonstationary magnetic and electric fields in a two-dimensional case is studied. The supercharges which are the integrals of motion and their algebra are established. Using the obtained algebra…

We investigate some fundamental features of a class of non-linear relativistic lagrangian field theories with kinetic self-coupling. We focus our attention upon theories admitting static, spherically symmetric solutions in three space…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

An asymptotic expansion is performed to obtain quasi-axisymmetric magnetic configurations that are weakly non-axisymmetric. A large space of solutions is identified, which satisfy the condition of quasi-axisymmetry on a single magnetic flux…

This manuscript is the first in a series of instalments that investigate spherically symmetric solutions within the effective dynamics program of Loop Quantum Gravity. The choice of lattice is adapted such that it remains invariant under a…