Nonlinear waves in media with complex dispersion: the example of nonlocal Sine-Gordon equation
By: G.L.Alfimov
From: Moscow Institute of Electronic Engineering, Zelenograd, Moscow, Russia
At: Instituto de Investigação Interdisciplinar, Anfiteatro
[2010-09-22]
It is quite typical of nonlinear wave models to include dispersion law as quadratic one. In many cases this approximation works well and allows to describe nonlinear excitations in the model quite completely. However, in some cases quadratic dispersion law is not adequate and should be replaced by more complex one. This situation needs more sophisticated mathematics, since the governing ODE (or PDE) of the model should be replaced by integrodifferential equations.
In the talk examples of such models will be given. The basic example, so called nonlocal Sine-Gordon equation, will be discussed in detail, including its applications in nonlocal Josephson electrodynamics and the approaches, both theoretical and numerical, for its analysis. It will be shown that switching from local to nonlocal model results in great difference of model features.