Accession Number:

ADA193268

Title:

Davey-Stewartson I - A Quantum 2+1 Dimensional Integrable System,

Descriptive Note:

Corporate Author:

CLARKSON UNIV POTSDAM NY INST FOR NONLINEAR STUDIES

Report Date:

1987-05-01

Pagination or Media Count:

14.0

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 21d 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 11-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.

Subject Categories:

  • Quantum Theory and Relativity

Distribution Statement:

APPROVED FOR PUBLIC RELEASE