Related papers: On Partial Differential and Difference Equations w…
We consider a system of partial differential equations, of interest to plasma physics, and provide all its Lie point symmetries, with their respective invariant solutions. We also discuss some of its conditional and partial symmetries. We…
In this short note we discuss ordinary differential equations which linearize upon one (or more) differentiations. Although the subject is fairly elementary, equations of this type arise naturally in the context of integrable systems.
The class of ordinary linear constant coefficient differential equations is naturally embedded into a wider class by associating differential equations to algebraic curves.
In this thesis, we study the one parameter point transformations which leave invariant the differential equations. In particular we study the Lie and the Noether point symmetries of second order differential equations. We establish a new…
We consider two natural gradings on the space of symmetric functions: by degree and by length. We introduce a differential operator $T$ that leaves the components of this double grading invariant and exhibit a basis of bihomogeneous…
We extend to manifolds endowed with a general geometric structure, the classical notions of gradient as well as Laplace operator, and provide some of their natural properties.
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
We define a symmetric derivative on an arbitrary nonempty closed subset of the real numbers and derive some of its properties. It is shown that real-valued functions defined on time scales that are neither delta nor nabla differentiable can…
An algorithm for studing the symmetrical properties of the partial differential equation of the type Lu=0 is proposed. By symmetry of this equation we mean the operators Q satisfying commutational relations of order p more than p=1 on the…
Symmetries play a very important r\^ole in Particle Physics. In extended scalar sectors, the existence of symmetries may permit the models to comply with the experimental constraints in a natural way, and at the same time reduce the number…
Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic influences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo-stable…
For nonstationary, strongly mixing sequences of random variables taking their values in a finite-dimensional Euclidean space, with the partial sums being normalized via matrix multiplication, with certain standard conditions being met, the…
We give a survey of results regarding existence and regularity for autonomous functionals of linear growth that depend on the symmetric rather than the full gradients.
Nonlinear PDE's having {\bf given} conditional symmetries are constructed. They are obtained starting from the invariants of the "conditional symmetry" generator and imposing the extra condition given by the characteristic of the symmetry.…
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…
We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary…
The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.
We study linear ordinary differential equations which are analytically parametrized on Hermitian symmetric spaces and invariant under the action of symplectic groups. They are generalizations of the classical Lam\'e equation. Our main…
A {\it Lie system} is a nonautonomous system of first-order differential equations admitting a {\it superposition rule}, i.e., a map expressing its general solution in terms of a generic family of particular solutions and some constants.…
It is shown that, under suitable conditions, involving in particular the existence of analytic constants of motion, the presence of Lie point symmetries can ensure the convergence of the transformation taking a vector field (or dynamical…