Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
Exactly Solvable and Integrable Systems
2009-11-13 v1
Abstract
A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared.
Keywords
Cite
@article{arxiv.nlin/0702020,
title = {Quasideterminant solutions of a non-Abelian Hirota-Miwa equation},
author = {C. R. Gilson and J. J. C. Nimmo and Y. Ohta},
journal= {arXiv preprint arXiv:nlin/0702020},
year = {2009}
}