Topological defects in 1D elastic waves

It has been recently shown theoretically that a topological defect in a 1D periodic potential may give rise to two localized states within the energy gaps. In this work we present an experimental realization of this effect for the case of torsional waves in elastic rods. We also show numerically that three, or even more, localized states can be present if the parameters characterizing the topological defect are suitably varied.Comment: 3 pages, 4 figures, accepted in Physica

Analytic Non-integrability in String Theory

Using analytic techniques developed for Hamiltonian dynamical systems we show that a certain classical string configurations in AdS_5 x X_5 with X_5 in a large class of Einstein spaces, is non-integrable. This answers the question of integrability of string on such backgrounds in the negative. We consider a string localized in the center of AdS_5 that winds around two circles in the manifold X_5.Comment: 14 page

Nonautonomous Hamiltonian Systems and Morales-Ramis Theory I. The Case x¨=f(x,t)\ddot{x}=f(x,t)

In this paper we present an approach towards the comprehensive analysis of the non-integrability of differential equations in the form $\ddot x=f(x,t)$ which is analogous to Hamiltonian systems with 1+1/2 degree of freedom. In particular, we analyze the non-integrability of some important families of differential equations such as Painlev\'e II, Sitnikov and Hill-Schr\"odinger equation. We emphasize in Painlev\'e II, showing its non-integrability through three different Hamiltonian systems, and also in Sitnikov in which two different version including numerical results are shown. The main tool to study the non-integrability of these kind of Hamiltonian systems is Morales-Ramis theory. This paper is a very slight improvement of the talk with the almost-same title delivered by the author in SIAM Conference on Applications of Dynamical Systems 2007.Comment: 15 pages without figures (19 pages and 6 figures in the published version