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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)
  • M Leo, R A Leo
  • 2007
We present a detailed numerical and analytical study of the stability properties of the N/4 (pi/2-mode) one-mode nonlinear solution of the Fermi-Pasta-Ulam-beta system. The numerical analysis is made as a function of the number N of the particles of the system and of the product lambda=epsilonbeta , where epsilon is the energy density and beta is the(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)
The relevance of Information and Communication Technologies (ICTs) is progressively increasing in every aspect of modern life. At the same time, the aging trend most European countries are experiencing, may significantly impact on their absorptive capacity of innovation, which is a key determinant of socioeconomic development, with deep policy implications(More)
In a recent paper [M. Leo, R. A. Leo, and P. Tempesta, J. Stat. Mech. (2011) P03003], it has been shown that the π/2-mode exact nonlinear solution of the Fermi-Pasta-Ulam β system, with periodic boundary conditions, admits two energy density thresholds. For values of the energy density ε below or above these thresholds, the solution is stable. Between them,(More)
We carry out a group-theoretical study of the pair of nonlinear Schrödinger equations describing the propagation of waves in nonlinear birefringent optical fibers. We exploit the symmetry algebra associated with these equations to provide examples of specific exact solutions. Among them, we obtain the soliton profile, which is related to the coordinate(More)
The relevance of Information and Communication Technologies (ICTs) is progressively increasing in every aspect of modern life. At the same time, the aging trend most European countries are experiencing, may significantly impact on their absorptive capacity of innovation, which is a key determinant of socioeconomic development, with deep policy implications(More)