ABSTRACT
An appealing idea of modern dynamics is that the complicated and apparently stochastic time behavior of large and even infinite-dimensional nonlinear systems is in fact a manifestation of a deterministic flow on a low dimensional chaotic attractor. The coherent spatial structures in problem are the solitary wave solutions of nonlinear partial differential equations which belong to a well known class of integrable or near integrable systems, namely, nonlinear Schrodinger type equations. The mathematical model describing the propagation of a laser beam in an optical ring cavity has been extensively discussed in the literature usually within the plane wave approximation. The numerical experiments show that the central part of the transverse fixed points is well approximated by solitary waves. However, the correct amplitude parameter is chosen by a numerical fitting procedure. The close connection between fixed points of the infinite dimensional map and fixed points of a reduced map in the solitary wave parameters is established.
