The stability of the one-mode nonlinear solutions of the Fermi-Pasta-Ulam beta system is numerically investigated. No external perturbation is considered for the one-mode exact analytical solutions, the only perturbation being that introduced by computational errors in the numerical integration of motion equations. The threshold energy for the excitation of… (More)
We show that certain infinitesimal operators of the Lie–point symmetries of the incompressible 3D Navier–Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and throws light on the alignment mechanism between the vorticity → ω and the vortex stretching vector S → ω,… (More)
The Estabrook-Wahlquist prolongation method is applied to the (compact and noncompact) continuous isotropic Heisenberg model in 1 + 1 dimensions. Using a special realization (an algebra of the Kac-Moody type) of the arising incomplete prolongation Lie algebra, a whole family of nonlinear field equations containing the original Heisenberg system is… (More)
We apply the (direct and inverse) prolongation method to a couple of non-linear Schrödinger equations. These are taken as a laboratory field model for analyzing the existence of a connection between the integrability property and loop algebras. Exploiting a realization of the Kac-Moody type of the incomplete prolongation algebra associated with the system… (More)
An algebraic method is devised to look for non-local symmetries of the pseudopotential type of nonlinear field equations. The method is based on the use of an infinite-dimensional subalgebra of the prolon-gation algebra L associated with the equations under consideration. Our approach, which is applied by way of example to the Dym and the Korteweg-de Vries… (More)
A system of equations of the reaction–diffusion type is studied in the framework of both the direct and the inverse prolongation structure. We find that this system allows an incomplete prolongation Lie algebra, which is used to find the spectral problem and a whole class of nonlinear field equations containing the original ones as a special case.
The Navier-Stokes-Fourier model for a 3D thermoconducting viscous fluid, where the evolution equation for the temperature T contains a term proportional to the rate of energy dissipation, is investigated analitically at the light of the rotational invariance property. Two cases are considered: the Cou-ette flow and a flow with a radial velocity between two… (More)