Davey-Stewartson I - A Quantum 2+1 Dimensional Integrable System,
Abstract
Davey-Stewartson I is a nonlinear evolution equation originally derived in the context of multidimensional weakly nonlinear water waves. It has recently been exactly solved by the classical inverse scattering method for localized potentials, and also possesses nonlocal soliton solutions. The authors have calculated Poisson bracket relations for elements of the scattering matrix, as well as corresponding quantum commutation relations. Commutation relations are found that are a 2+1d generalization of a Yang-Baxter algebra. Exactly solvable systems have played a significant role in our understanding of nonperturbative phenomena in physics. Many quantum field theories in 1+1-dimensions have been found to be integrable, enabling the calculation of exact S-matrices and physical spectra. The Ising model and other exactly solvable models of 2-dimensional statistical mechanics have helped to provide a basis for modern scaling theory. Moreover, some of the more interesting mathematics occurring in quantum string theories, including loop spaces and Kac-Moody-Virasoro algebras, also appear in integrable systems.
Document Details
- Document Type
- Technical Report
- Publication Date
- May 01, 1987
- Accession Number
- ADA193268
Entities
People
- C. L. Schultz
- D. B. Yaacov
- M. J. Ablowitz
Organizations
- Clarkson University