Miura Reciprocal transformation for two integrable hierarchies in 1+1 dimensions
Mathematical Physics
2013-01-17 v1 math.MP
Exactly Solvable and Integrable Systems
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.
Keywords
Cite
@article{arxiv.1301.3636,
title = {Miura Reciprocal transformation for two integrable hierarchies in 1+1 dimensions},
author = {P. G. Estevez and C. Sardon},
journal= {arXiv preprint arXiv:1301.3636},
year = {2013}
}