183 citations · 679 across the 24 of their papers we have counts for
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Bäcklund Transformations and the Atiyah-Ward ansatz for Noncommutative Anti-Self-Dual Yang-Mills Equations
Claire R. Gilson, Masashi Hamanaka, Jonathan J. C. Nimmo
We present Backlund transformations for the noncommutative anti-self-dual Yang-Mills equation where the gauge group is G=GL(2) and use it to generate a series of exact solutions fr…
Matrix solutions of a noncommutative KP equation and a noncommutative mKP equation
C. R. Gilson, J. J. C. Nimmo, C. M. Sooman
Matrix solutions of a noncommutative KP and a noncommutative mKP equation which can be expressed as quasideterminants are discussed. In particular, we investigate interaction prope…
On solutions to the non-Abelian Hirota-Miwa equation and its continuum limits
C. X. Li, J. J. C. Nimmo, K. M. Tamizhmani
In this paper, we construct grammian-like quasideterminant solutions of a non-Abelian Hirota-Miwa equation. Through continuum limits of this non-Abelian Hirota-Miwa equation and it…
A noncommutative semi-discrete Toda equation and its quasideterminant solutions
C. X. Li, J. J. C. Nimmo
A noncommutative version of the semi-discrete Toda equation is considered. A Lax pair and its Darboux transformations and binary Darboux transformations are found and they are used…