Collective Properties of Neural Systems and Their Relation to Other Physical Models
Abstract
During the tenure of this contract progress was accomplished on three fronts: 1) The recursion operator of the Landau-Lifshitz equation has been completed explicitly. This has been achieved algorithmically by utilizing methods introduced earlier. It should be emphasized that in addition to the important implications of these results to general lattice theories and neural networks, the answers obtained are novel on their own merit since textbooks referred to constructing the above recursion operation as an outstanding open problem. 2) We have continued our study of nonlinear optics. We have introduced a new system of nonlinear PDE's that governs the development path of photoresist fabrication. We have employed a proof given in collaboration with Araki concerning an iteration scheme, used throughout the analysis. We have reported this work in various publications and in a number of international conferences. 3) Substantial progress has been made towards solving the nonlinear Schrodinger (NLS) equation on the half-time. Finite boundedness in conjunction with nonlinear evolution equations have alluded investigators for years. Since nonlinear optics is to be employed on finite boundaries, a major thrust was needed to achieve viable results. A new method has been introduced and tested on the NLS on the half-line. For the first time concrete analytical results have been obtained, and the entire problem has been reduced to linearizing a certain equation satisfied by the scattering data. This linearization and the application of the above method to other important evolution equations is under investigation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 05, 1988
- Accession Number
- ADA199988
Entities
People
- A. S. Fokas
- Eytan Barouch
Organizations
- Clarkson University