183 citations · 679 across the 24 of their papers we have counts for
21 papers · 1 filter
Soliton Solutions of Noncommutative Anti-Self-Dual Yang-Mills Equations
Claire R. Gilson, Masashi Hamanaka, Shan-Chi Huang +1
We present exact soliton solutions of anti-self-dual Yang-Mills equations for G=GL(N) on noncommutative Euclidean spaces in four-dimension by using the Darboux transformations. Gen…
Linearization of the box-ball system: an elementary approach
Saburo Kakei, Jonathan J. C. Nimmo, Satoshi Tsujimoto +1
Kuniba, Okado, Takagi and Yamada have found that the time-evolution of the Takahashi-Satsuma box-ball system can be linearized by considering rigged configurations associated with…
Darboux and Binary Darboux Transformations for Discrete Integrable Systems. II. Discrete Potential mKdV Equation
Ying Shi, Jonathan Nimmo, Junxiao Zhao
The paper presents two results. First it is shown how the discrete potential modified KdV equation and its Lax pairs in matrix form arise from the Hirota-Miwa equation by a 2-perio…
Binary Darboux Transformation for the Sasa-Satsuma Equation
Jonathan J. C. Nimmo, Halis Yilmaz
The Sasa-Satsuma equation is an integrable higher-order nonlinear Schrödinger equation. Higher-order and multicomponent generalisations of the nonlinear Schrödinger equation are im…
Quasideterminant solutions to a noncommutative -difference two-dimensional Toda lattice equation
Chun-Xia Li, Jonathan Nimmo, Shou-Feng Shen
In [1], a generalized type of Darboux transformations defined in terms of a twisted derivation was constructed in a unified form. Such twisted derivations include regular derivatio…
On Darboux transformations for the derivative nonlinear Schrödinger equation
Jonathan J. C. Nimmo, Halis Yilmaz
We consider Darboux transformations for the derivative nonlinear Schrödinger equation. A new theorem for Darboux transformations of operators with no derivative term are presented…
Darboux and binary Darboux transformations for discrete integrable systems 1. Discrete potential KdV equation
Ying Shi, Jonathan J C Nimmo, Da-jun Zhang
The Hirota-Miwa equation can be written in `nonlinear' form in two ways: the discrete KP equation and, by using a compatible continuous variable, the discrete potential KP equation…
Darboux transformations for a twisted derivation and quasideterminant solutions to the super KdV equation
C. X. Li, J. J. C. Nimmo
This paper is concerned with a generalized type of Darboux transformations defined in terms of a twisted derivation satisfying where is a homomorphism. S…
Yang-Baxter Maps from the Discrete BKP Equation
Saburo Kakei, Jonathan J. C. Nimmo, Ralph Willox
We construct rational and piecewise-linear Yang-Baxter maps for a general N-reduction of the discrete BKP equation.
Tzitzeica solitons vs. relativistic Calogero-Moser 3-body clusters
J. J. C. Nimmo, S. N. M. Ruijsenaars
We establish a connection between the hyperbolic relativistic Calogero-Moser systems and a class of soliton solutions to the Tzitzeica equation (aka the Dodd-Bullough-Zhiber-Shabat…
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…
Quasideterminant solutions of a non-Abelian Toda lattice and kink solutions of a matrix sine-Gordon equation
C. X. Li, J. J. C. Nimmo
Two families of solutions of a generalized non-Abelian Toda lattice are considered. These solutions are expressed in terms of quasideterminants, constructed by means of Darboux and…
On a direct approach to quasideterminant solutions of a noncommutative modified KP equation
C. R. Gilson, J. J. C. Nimmo, C. M. Sooman
A noncommutative version of the modified KP equation and a family of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means…
Bäcklund Transformations 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…
Quasideterminant solutions of a non-Abelian Hirota-Miwa equation
C. R. Gilson, J. J. C. Nimmo, Y. Ohta
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 express…
On a direct approach to quasideterminant solutions of a noncommutative KP equation
C. R. Gilson, J. J. C. Nimmo
A noncommutative version of the KP equation and two families of its solutions expressed as quasideterminants are discussed. The origin of these solutions is explained by means of D…
On pattern structures of the N-soliton solution of the discrete KP equation over a finite field
Mariusz Bialecki, Jonathan J C Nimmo
The existence and properties of coherent pattern in the multisoliton solutions of the dKP equation over a finite field is investigated. To that end, starting with an algebro-geomet…
A relationship between rational and multi-soliton solutions of the BKP hierarchy
J. J. C. Nimmo, A. Yu. Orlov
We consider a special class of solutions of the BKP hierarchy which we call -functions of hypergeometric type. These are series in Schur -functions over partitions, with coef…
The Sasa-Satsuma higher order nonlinear Schrodinger equation and its bilinearization and multi-soliton solutions
C. Gilson, J. Hietarinta, J. Nimmo +1
Higher order and multicomponent generalizations of the nonlinear Schrodinger equation are important in various applications, e.g., in optics. One of these equations, the integrable…