Nonlinear Waves: Coherence, Chaos, Pattern Formation, and Geometry
Abstract
Coherence and chaos in partial differential equations was studied, with particular emphasis on the damped-driven sine Gordon equation and an optically bistable laser cavity. The propagation of rapidly oscillating nonlinear integrable waves was investigated. The results about propagation in an optically bistable ring cavity the identification of the interplay between coherent transverse spatial structures and temporal chaos in the characteristics of the laser beam. Principal mathematical results on the damped-driven sine- Gordon equation include a numerical study of low dimensional chaotic attractors with coherent spatial structures, including dynamical system diagnostics of their time series, and direct numerical measurements establishing that the attractor is well co-ordinatized by a few nonlinear normal modes; complete analytical identification of all homoclinic structures for the integrable sine- Gordon equation; direct numerical detection of homoclinic crossings along the chaotic attractor of the full syste,. Principal mathematical results about the propagation of rapidly oscillating integrable waves include the identification and derivation of a Hamiltonian structure for the modulation equations and a study of the process by which singularities are smoothed by dispersion through the injection of additional degrees of freedom into the field.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jun 01, 1988
- Accession Number
- ADA198235
Entities
People
- Hermann Flaschka
Organizations
- University of Arizona