Past Seminars Seminários Já Decorridos 2014

Phenomenon of “sliding velocities” in nonlinear dispersive models

By: Georgy Alfimov
From: National Research University of Electronic Technology (MIET), Moscow, Zelenograd, Russia
At: Instituto de Investigação Interdisciplinar, Anfiteatro
[2014-10-16] 14:00

The talk is devoted to localized waves (kink-like excitations or solitary pulses) in nonlinear dispersive media. The propagation of these waves is described by nonlinear equation of Klein-Gordon or Korteweg-de Vries type. The complex dispersion of the medium is modeled by incorporating of nonlocal terms in the governing equations. It is known that, typically, the nonlocality reduces the mobility of nonlinear waves. In many physically relevant examples a localized wave launched with some velocity in such a dispersive medium loses energy through radiation, slows down and eventually stops. However, there are other examples where localized waves can travel with some specific (“privileged”) velocities to great distances. These velocities, called also “sliding velocities”, are important characteristics of the medium.

In the talk, some examples of nonlinear systems where sliding velocities exist are given. In all these cases these velocities constitute discrete set. In the limit of weak nonlocality it is conjectured that the asymptotics of this set is related to the type and the location of singularities in the complex plane of the solution in local unperturbed system. This conjecture is strongly confirmed by results of numerical computation.