|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Integrable Equations on Time Scales | | Metin Gurses
; Gusein Sh. Guseinov
; Burcu Silindir
; | | Date: |
27 Jul 2005 | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI | | Abstract: | Integrable systems are usually given in terms of functions of continuous variables (on ${mathbb R}$), functions of discrete variables (on ${mathbb Z}$) and recently in terms of functions of $q$-variables (on ${mathbb K}_{q}$). We formulate the Gel’fand-Dikii (GD) formalism on time scales by using the delta differentiation operator and find more general integrable nonlinear evolutionary equations. In particular they yield integrable equations over integers (difference equations) and over $q$-numbers ($q$-difference equations). We formulate the GD formalism also in terms of shift operators for all regular-discrete time scales. We give a method to construct the recursion operators for integrable systems on time scales. Finally, we give a trace formula on time scales and then construct infinitely many conserved quantities (Casimirs) of the integrable systems on time scales. | | Source: | arXiv, nlin.SI/0507061 | | 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