Related papers: Contact germs and partial differential equations
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…
We present here the explicit parametric solutions of second order differential equations invariant under time translation and rescaling and third order differential equations invariant under time translation and the two homogeneity…
A generalization of exterior calculus is considered by allowing the partial derivatives in the exterior derivative to assume fractional orders. That is, a fractional exterior derivative is defined. This is found to generate new vector…
The study of integrability of the mathematical physics equations showed that the differential equations describing real processes are not integrable without additional conditions. This follows from the functional relation that is derived…
A new, conceptual proof approach for establishing the existence of regenerative space-time points for symmetric, translation invariant, finite-range interaction contact processes on survival is shown. The proof is elementary, complements…
We classify contact manifolds $(M,\mathcal D)$ which are homogeneous under a connected semisimple Lie group $G$, and symmetric in the sense that there exists a contactomorphism of $(M,\mathcal D)$ normalizing $G$, fixing a point $o$ in $M$…
This overview focuses on the notion of partial dynamical symmetry (PDS), for which a prescribed symmetry is obeyed by a subset of solvable eigenstates, but is not shared by the Hamiltonian. General algorithms are presented to identify…
We investigate the local dynamics of antiholomorphic diffeomorphisms around a parabolic fixed point. We first give a normal form. Then we give a complete classification including a modulus space for antiholomorphic germs with a parabolic…
We define and study fractional versions of the well-known Gamma subordinator $\Gamma :=\{\Gamma (t),$ $t\geq 0\},$ which are obtained by time-changing $% \Gamma $ by means of an independent stable subordinator or its inverse. Their…
Giving a new form of the vortex mode equation by a proper change of parameter, our aim is to analyze the point and contact symmetries of the new equation. Fundamental invariants and a form of general solutions of point transformations along…
A systematic and unified approach to transformations and symmetries of general second order linear parabolic partial differential equations is presented. Equivalence group is used to derive the Appell type transformations, specifically…
Contact has been well established as an important quantity to govern dilute quantum systems, in which the pairwise correlation at short distance traces a broad range of thermodynamic properties. So far, studies have been focusing on contact…
Using the notion of aggregation work, we construct a system of differential equations for the aggregation number of micelles which is a function of the parameters of micellization (parametric equations). There are explicit solutions for two…
We discuss some recent advances concerning the symmetry of stochastic differential equations, and in particular the interrelations between these and the integrability -- complete or partial -- of the equations.
We study the interplay between geometry and partial differential equations. We show how the fundamental ideas we use require the ability to correctly calculate the dimensions of spaces associated to the varieties of zeros of the symbols of…
Lagrangian contact supersymmetries (depending on derivatives of arbitrary order) are treated in very general setting. The cohomology of the variational bicomplex on an arbitrary graded manifold and the iterated cohomology of a generic…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
We consider several aspects of conjugating symmetry methods, including the method of invariants, with an asymptotic approach. In particular we consider how to extend to the stochastic setting several ideas which are well established in the…
The explicit form of conformal generators is found which provides the extension of Poincare symmetry for massless particles of arbitrary helicity. The helicity 1/2 particles are considered as the particular example. The realization of…
Infinitesimal symmetries of a partial differential equation (PDE) can be defined algebraically as the solutions of the linearization (Frechet derivative) equation holding on the space of solutions to the PDE, and they are well-known to…