Miura type transformations and homogeneous spaces

Details Miura type transformations and homogeneous spaces Miura type transformations and homogeneous spaces

2004-12-14

arxiv.org/abs/nlin/0412036v3

J. Phys. A: Math. Gen. 38 (2005) 4433-4446

Nonlinear Sciences

Exactly Solvable and Integrable Systems

17 pages; v3, v2: minor improvements

Scientific paper

10.1088/0305-4470/38/20/010

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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