Błaszak, M. and Szablikowski, B.M. (2009) ClassicalR-matrix theory for bi-Hamiltonian field systems. Journal of Physics A: Mathematical and Theoretical, 42(40), p. 404002. (doi: 10.1088/1751-8113/42/40/404002)
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Publisher's URL: http://dx.doi.org/10.1088/1751-8113/42/40/404002
Abstract
This is a survey of the application of the classical R-matrix formalism to the construction of infinite-dimensional integrable Hamiltonian field systems. The main point is the study of bi-Hamiltonian structures. Appropriate constructions on Poisson, noncommutative and loop algebras as well as the central extension procedure are presented. The theory is developed for (1+1)- and (2+1)-dimensional field and lattice soliton systems as well as hydrodynamic systems. The formalism presented contains sufficiently many proofs and important details to make it self-contained and complete. The general theory is applied to several infinite-dimensional Lie algebras in order to construct both dispersionless and dispersive (soliton) integrable field systems.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Szablikowski, Dr Blazej |
| Authors: | Błaszak, M., and Szablikowski, B.M. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Physics A: Mathematical and Theoretical |
| ISSN: | 1751-8113 |
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