|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
27 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Toroidal Lie algebras and Bogoyavlensky's 2+1-dimensional equation | | T. Ikeda
; K. Takasaki
; | | Date: |
10 Apr 2000 | | Journal: | Internat. Math. Res. Notices 2001, No. 7, 329-369 | | Subject: | Exactly Solvable and Integrable Systems; Quantum Algebra | nlin.SI hep-th math.QA | | Abstract: | We introduce an extension of the ell-reduced KP hierarchy, which we call the ell-Bogoyavlensky hierarchy. Bogoyavlensky’s 2+1-dimensional extension of the KdV equation is the lowest equation of the hierarchy in case of ell=2. We present a group-theoretic characterization of this hierarchy on the basis of the 2-toroidal Lie algebra sl_ell^{tor}. This reproduces essentially the same Hirota bilinear equations as those recently introduced by Billig and Iohara et al. We can further derive these Hirota bilinear equation from a Lax formalism of the hierarchy.This Lax formalism also enables us to construct a family of special solutions that generalize the breaking soliton solutions of Bogoyavlensky. These solutions contain the N-soliton solutions, which are usually constructed by use of vertex operators. | | Source: | arXiv, nlin.SI/0004015 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER