A Non-Commutative Semi-Discrete Toda Equation and Its Quasi-Determinant Solutions

Li, C. X.; Nimmo, J. J. C.

doi:10.1017/s0017089508004837

Cited by 6 publications

(2 citation statements)

References 23 publications

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“…The quasideterminants play important roles in the construction of noncommutative soliton solutions not only for the noncommutative anti-self-dual Yang-Mills equation, but also for various lower-dimensional noncommutative integrable equations [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Noncommutative solitons and quasideterminants

Hamanaka¹

2014

Phys. Scr.

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We discuss an extension of soliton theory and integrable systems to noncommutative spaces, focusing on integrable aspects of noncommutative anti-self-dual Yang-Mills equations. We give a wide class of exact solutions by solving a Riemann-Hilbert problem for the Atiyah-Ward ansatz and present Bäcklund transformations for the G = U(2) noncommutative anti-self-dual Yang-Mills equations. We find that one kind of noncommutative determinant, quasideterminants, play crucial roles in the construction of noncommutative solutions. We also discuss reduction of a noncommutative anti-self-dual Yang-Mills equation to noncommutative integrable equations. This is partially based on a collaboration with C.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Noncommutative solitons and quasideterminants

Hamanaka¹

2014

Phys. Scr.

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“…Then, we will show how the rules of these confluent algorithms lead us to coupled non-Abelian lattice equations, in particular to some extensions of the Lotka-Volterra system, in the style of the equation related to the confluent form of the scalar ε-algorithm. Obviously, the exact relations between non-scalar convergence acceleration algorithms and non-commutative integrable systems (described, for example, in [14]) remain to be discovered.…”

Section: Introduction and Motivationsmentioning

confidence: 99%