Fecha: Lunes 15 de marzo de 2010
Lugar: Facultad de Ciencias. Seminario del Dpto. de Física Atómica, Molecular y Nuclear (3ª planta de Físicas)
Horario: 12h.
Descripción: Conferencia Nonlinear Schrödinger solitons under spatio-temporal forces, and a new stability criterion a cargo del Prof. Franz G. Mertens. University of Bayreuth (Bayreuth, Alemania).
Resumen de la conferencia: We investigate the dynamics of solitons of the Nonlinear Schrödinger Equation (NLSE) with the following perturbations: spatio-temporal forces of the form f(x,t) = a exp[i K(t) x] and damping. Such forces have applications in nonlinear optical waveguide arrays.
Using a Lagrangian approach, which is generalized by the introduction of a dissipation function, we develop a Collective-Coordinate-Theory which yields ODEs for the collective coordinates position, velocity, amplitude and phase of the soliton. The ODEs are solved analytically and numerically for the following cases: constant, harmonic and biharmonic K(t). In the first case the spatial average of f(x) vanishes, nevertheless the soliton performs on the average a unidirectional motion. Interestingly, the oscillations of the soliton position around the average motion are much smaller than the period of f(x). In the biharmonic case the soliton performs a ratchet motion.
We conjecture a new stability criterion: if the curve P(V), where P(t) and V(t) are the soliton momentum and velocity, has a branch with negative slope, the soliton is predicted to become unstable which is confirmed by our simulations for the perturbed NLSE. Moreover, this curve also yields a good estimate for the soliton lifetime: the shorter the branch with negative slope is, the longer the soliton lives.
Organiza: Instituto Carlos I de Fisica Teorica y Computacional
Dpto. de Fisica Atomica Molecular y Nuclear
Dpto. de Fisica Atomica Molecular y Nuclear