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Miura Reciprocal transformation for two integrable hierarchies in 1+1 dimensions

We here present two different hierarchies of PDEs in 1+1 dimensions whose first and second member are the shallow water wave Camassa-Holm and Qiao equations, correspondingly. These two hierarchies can be transformed by reciprocal methods into the Calogero-Bogoyanlevski-Schiff equation (CBS) and its modified version (mCBS), respectively. Considering that there exists a Miura transformation between the CBS and mCBS, we shall obtain a relation between the initial hierarchies by means of a composition of a Miura and reciprocal transforms.

preprint2013arXivOpen access
P. G. EstevezC. Sardon
math-phmath.MPnlin.SI
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P. G. EstevezC. Sardon

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