Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

Gilson, C.R., Nimmo, J.J.C. and Ohta, Y. (2007) Quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Journal of Physics A: Mathematical and Theoretical, 40(42), pp. 12607-12617. (doi: 10.1088/1751-8113/40/42/S07)

Abstract

A non-Abelian version of the Hirota–Miwa equation is considered. In an earlier paper of Nimmo (2006 J. Phys. A: Math. Gen. 39 5053–65) 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-Plücker coordinates and that the non-Abelian Hirota–Miwa equation may be written as a quasi-Plücker relation. The special case of the matrix Hirota–Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Gilson, Dr Claire and Nimmo, Dr Jonathan
• Authors: Gilson, C.R., Nimmo, J.J.C., and Ohta, Y.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Journal of Physics A: Mathematical and Theoretical
• ISSN: 1751-8113
• ISSN (Online): 1751-8121