Nonlinear Wave Propagation
Abstract
We have been pursuing a number of research problems including: 1) Development of solutions to multidimensional nonlinear evolution equations of physical significance. Prototypes are the so-called Kadomtsev-Petviashvilli and Davey-Stewartson equations. The nature of the boundary value problems and solutions of the equation in the so-called strong coupling limit have recently been uncovered. 2) Solutions of discrete nonlinear evolutions. In our studies we have found the following surprising situation -- associated with the integrable nonlinear Schrodinger equations are standard numerical schemes which exhibit at intermediate levels of mesh refinement a weak form of temporal chaos. Differences schemes developed by Inverse Scattering Transform (IST) methods do not exhibit this spurious chaos. All schemes agree when the mesh is sufficiently refined. 3) Inverse problems associated with multidimensional problems. A key element in this work is the DBAR method which has been extended from the study of two dimensional inverse problems, geophysics and acoustics. 4) The principal investigator and his associates have been studying a class of cellular automata which admit solitons interaction. These systems are not reversible, which is quite a novel and interesting aspect. (edc)
Document Details
- Document Type
- Technical Report
- Publication Date
- May 22, 1989
- Accession Number
- ADA215500
Entities
People
- M. Ablowitz
Organizations
- Clarkson University