The Generation and Propagation of Oscillations in NonLinear Systems.
Abstract
The propagation of dispersive nonlinear waves in continuous and discrete media is investigated. The small scale dispersive oscillations are averaged out and a complete set of modulation equations that describe the evolution of the macroscopic quantities are derived and in special cases solved. At the level of greater refinement. detailed information on the small scale structure is obtained in integrable models. This is made possible by the development of a powerful new technique that leads to the explicit asymptotic solution of Riemann-Hilbert problems. Other techniques employed include Liapounov-Schmidt decomposition, modulation theory, eigenvalue dynamics, stability analysis, and shock wave theory. Models analyzed include the integrable as well as the generalized nonitegrable Korteweg-de Vries equation, the (modulationally unstable) nonlinear Schroedinger equation, and particle chains under various types of forcing. Semiconductor instabilities are also investigated. which lead to the generation of time periodic waves in semiconductors upon appropriate dc voltage bias. The nature of the instability that drives such time periodic behavior is explained and the phenomena are analyzed and understood by the use of analytical and computational means.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 19, 1996
- Accession Number
- ADA316746
Entities
People
- Stephanos Venakides
Organizations
- Duke University