The dynamics of N point vortices in a fluid is described by the Helmholtz-Kirchhoff (HK) equations which lead to a completely integrable Hamiltonian system for N=2 or 3 but chaotic dynamics for N>3. Here we consider a generalization of the HK equatio
ns to describe the dynamics of magnetic vortices within a collective-coordinate approximation. In particular, we analyze in detail the dynamics of a system of three magnetic vortices by a suitable generalization of the solution for three point vortices in an ordinary fluid obtained by Groebli more than a century ago. The significance of our results for the dynamics of ferromagnetic elements is briefly discussed.
We consider the spatiotemporal evolution of a wave packet in disordered nonlinear Schrodinger and anharmonic oscillator chains. In the absence of nonlinearity all eigenstates are spatially localized with an upper bound on the localization length (And
erson localization). Nonlinear terms in the equations of motion destroy Anderson localization due to nonintegrability and deterministic chaos. At least a finite part of an initially localized wave packet will subdiffusively spread without limits. We analyze the details of this spreading process. We compare the evolution of single site, single mode and general finite size excitations, and study the statistics of detrapping times. We investigate the properties of mode-mode resonances, which are responsible for the incoherent delocalization process.
