Dressing for a vector modified KdV hierarchy
Abstract
We present the hierarchy and soliton solutions associated to a multi-component generalisation of the modified Korteweg-de Vries equation. A recursive formula for obtaining the Lax operators associated to the higher flows of the hierarchy is provided. Using the method of rational dressing and the symmetries of the Lax operators we obtain the one-soliton solution. We also derive the general rank one-breather solution and express it in terms of determinants. We present the simplest case of the one-breather solution, which is parametrised by two constant unit vectors normal to each other. Finally, we obtain the associated B\"acklund transformation for the hierarchy.
Cite
@article{arxiv.2001.05301,
title = {Dressing for a vector modified KdV hierarchy},
author = {Panagiota Adamopoulou and Georgios Papamikos},
journal= {arXiv preprint arXiv:2001.05301},
year = {2020}
}
Comments
8 pages, based on a talk given by PA in XIth International Symposium: Quantum Theory and Symmetries, July 2019, Montreal, Canada