Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2011
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1103.3966 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Table of Contents:
- A 3-dimensional reduction of the seld-dual Yang-Mills (SDYM) equation, named SDYM3, is examined from the point of view of its symmetry and integrability characteristics. By using a non-auto-Backlund transformation, this equation is connected to its potential form (PSDYM3) and a certain isomorphism between the Lie algebras of symmetries of the two systems is shown to exist. This isomorphism allows us to study the infinite-dimensional Lie algebraic structure of the "potential symmetries" of SDYM3 by examining the symmetry structure of PSDYM3 (which is an easier task). By using techniques described in a recent paper, the recursion operators for both SDYM3 and PSDYM3 are derived. Moreover, a Lax pair and an infinite set of nonlocal conservation laws for SDYM3 are found, reflecting the fact that SDYM3 is a totally integrable system. This system may physically represent gravitational fields or chiral fields.