Miura type transformations and homogeneous spaces
Exactly Solvable and Integrable Systems
2009-11-10 v3 Mathematical Physics
Differential Geometry
math.MP
Abstract
We relate Miura type transformations (MTs) over an evolution system to its zero-curvature representations with values in Lie algebras g. We prove that certain homogeneous spaces of g produce MTs and show how to distinguish these spaces. For a scalar translation-invariant evolution equation this allows to classify all MTs in terms of homogeneous spaces of the Wahlquist-Estabrook algebra of the equation. For other evolution systems this allows to construct some MTs. As an example, we study MTs over the KdV equation, a 5th order equation of Harry-Dym type, and the coupled KdV-mKdV system of Kersten and Krasilshchik.
Keywords
Cite
@article{arxiv.nlin/0412036,
title = {Miura type transformations and homogeneous spaces},
author = {Sergey Igonin},
journal= {arXiv preprint arXiv:nlin/0412036},
year = {2009}
}
Comments
17 pages; v3, v2: minor improvements