Abstract
The application of the Gardner method for the generation of conservation laws to all the ABS equations is considered. It is shown that all the necessary information for the application of the Gardner method, namely Bäcklund transformations and initial conservation laws, follows from the multidimensional consistency of ABS equations. We also apply the Gardner method to an asymmetric equation which is not included in the ABS classification. An analog of the Gardner method for the generation of symmetries is developed and applied to the discrete Korteweg-de Vries equation. It can also be applied to all the other ABS equations.
| Original language | English |
|---|---|
| Article number | 235201 |
| Journal | Journal of Physics A: Mathematical and Theoretical |
| Volume | 43 |
| Issue number | 23 |
| DOIs | |
| State | Published - 2010 |
| Externally published | Yes |
Fingerprint
Dive into the research topics of 'Infinitely many symmetries and conservation laws for quad-graph equations via the Gardner method'. Together they form a unique fingerprint.Cite this
- APA
- Author
- BIBTEX
- Harvard
- Standard
- RIS
- Vancouver