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Miura type transformations and homogeneous spaces

Sergey Igonin
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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.

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Sergey Igonin. 2005-05-10. Miura type transformations and homogeneous spaces. https://doi.org/10.1088/0305-4470%2F38%2F20%2F010

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