Stability of periodic optical solitons for a nonlinear Schrodinger system

This paper is concerned with the existence and nonlinear stability of periodic travelling-wave solutions for a nonlinear Schrodinger-type system arising in nonlinear optics. We show the existence of smooth curves of periodic solutions depending on the dnoidal-type functions. We prove stability results by perturbations having the same minimal wavelength, and instability behaviour by perturbations of two or more times the minima period. We also establish global well posedness for our system by using Bourgain`s approach.

ENERGY OF GLOBAL FRAMES

The energy of a unit vector field X on a closed Riemannian manifold M is defined as the energy of the section into T(1) M determined by X. For odd-dimensional spheres, the energy functional has an infimum for each dimension 2k + 1 which is not attained by any non-singular vector field for k > 1. For k = 1, Hopf vector fields are the unique minima. In this paper we show that for any closed Riemannian manifold, the energy of a frame defined on the manifold, possibly except on a finite subset, admits a lower bound in terms of the total scalar curvature of the manifold. In particular, for odd-dimensional spheres this lower bound is attained by a family of frames defined on the sphere minus one point and consisting of vector fields parallel along geodesics.

A three-state model for the photophysics of guanine

The nonadiabatic photochemistry of the guanine molecule (2-amino-6-oxopurine) and some of its tautomers has been studied by means of the high-level theoretical ab initio quantum chemistry methods CASSCF and CASPT2. Accurate computations, based by the first time on minimum energy reaction paths, states minima, transition states, reaction barriers, and conical intersections on the potential energy hypersurfaces of the molecules lead to interpret the photochemistry of guanine and derivatives within a three-state model. As in the other purine DNA nucleobase, adenine, the ultrafast subpicosecond fluorescence decay measured in guanine is attributed to the barrierless character of the path leading from the initially populated (1)(pi pi* L-a) spectroscopic state of the molecule toward the low-lying methanamine-like conical intersection (gs/pi pi* L-a)(CI). On the contrary, other tautomers are shown to have a reaction energy barrier along the main relaxation profile. A second, slower decay is attributed to a path involving switches toward two other states, (1)(pi pi* L-b) and, in particular, (1)(n(o)pi*), ultimately leading to conical intersections with the ground state. A common framework for the ultrafast relaxation of the natural nucleobases is obtained in which the predominant role of a pi pi*-type state is confirmed.