Chaos and coherent structures in partial differential equations
The general purpose of this paper is the understanding of nonpredictable behaviour in nonlinear partial differential equations which have, in certain parameter ranges, the qualitative property of solution sensitivity with respect to initial conditions. More particularly, the authors explore the appealing idea of modern dynamics that the apparently stochastic time behaviour of large and even infinite-dimensional nonlinear systems is in fact a manifestation of a deterministic solution orbit on a low-dimensional chaotic attractor. Then a natural question concerns the possibility and the methods of identification of some physical characteristics such as the spatial structure of those few active modes dominating the dynamics. It is essentially to this problem that the paper is devoted. The authors begin with a set of governing equations and derive from it a simpler system which uniformly captures the dynamical behaviour of the former. The achievement of this plan is carried out by using fully nonlinear systems which are close to exactly integrable. The specific situation considered here is that of long term behaviour of electromagnetic waves in nonlinear passive optical cavities.
nonlinear partial differential equations
scientific article; zbMATH DE number 3960609
scientific article