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arXiv · 1301.3636

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

P. G. Estevez·C. Sardon
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Abstract

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.

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BibTeXRIS

P. G. Estevez, C. Sardon. 2013-01-16. Miura Reciprocal transformation for two integrable hierarchies in 1+1 dimensions. https://arxiv.org/abs/1301.3636

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