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Miura-reciprocal transformations for non-isospectral Camassa-Holm hierarchies in $2+1$ dimensions

We present two hierarchies of partial differential equations in $2+1$ dimensions. Since there exist reciprocal transformations that connect these hierarchies to the Calogero-Bogoyavlenski-Schiff equation and its modified version, we can prove that one of the hierarchies can be considered as a modified version of the other. The connection between them can be achieved by means of a combination of reciprocal and Miura transformations.

preprint2015arXivOpen access
P. G. EstévezC. Sardón
math-phmath.MP
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P. G. EstévezC. Sardón

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