183 citations · 679 across the 24 of their papers we have counts for
24 papers
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…
Darboux dressing and undressing for the ultradiscrete KdV equation
Jonathan J. C. Nimmo, Claire R. Gilson, R. Willox
We solve the direct scattering problem for the ultradiscrete Korteweg de Vries (udKdV) equation, over for any potential with compact (finite) support, by explicitly con…
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…