ISSN:
1420-9039
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract In many finite and infinite dimensional systemslow-dimensional behaviour is often observed. That is to say, the dynamics, observed experimentally or numerically, looks as if it can be described (approximately) with only a few essential parameters. Choosing the correct set of such “robust observables” is an essential ingredient of a successful low dimensional description. This paper reports on a specific example of a more general approach that aims at describing certain (low dimensional) phenomena in (high dimensional) damped/driven equations with parameters that are essentially determined from the underlying conservative part of the equation. In particular, a Hamiltonian or a Poisson structure of the conservative part is exploited to find (characterize) families of exact solutions. These solutions are then used as the “base functions” with the aid of which the solutions of the disturbed system are approximated. This approximation is accomplished using the parameters that characterize the family as variables that depend on time. In this paper, this procedure is applied to a class of systems which admit travelling waves when dissipation is ignored.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00945953
Permalink