183 citations · 807 across the 19 of their papers we have counts for
19 papers
Quasi-Pfaffian Solutions to Integrable Systems via Sylvester-Moutard Transformations
Claire R Gilson, Chen Shu
In this paper, we introduce a mathematical structure called the quasiPfaffian. The quasiPfaffian is analogous to the quasideterminant, a structure used instead of a determinant in…
Matrix-valued -deformed bi-orthogonal polynomials, Non-commutative Toda theory and Bäcklund transformation
Claire Gilson, Shi-Hao Li, Ying Shi
This paper is devoted to revealing the relationship between matrix-valued -deformed bi-orthogonal polynomials and non-commutative Toda-type hierarchies. In this procedure, Wrons…
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…
Statistics of photon-subtracted and photon-added states
Stephen M. Barnett, Gergely Ferenczi, Claire R. Gilson +1
The subtraction or addition of a prescribed number of photons to a field mode does not, in general, simply shift the probability distribution by the number of subtracted or added p…
Dromion solutions of noncommutative Davey-Stewartson equations
Claire R. Gilson, Susan R. Macfarlane
We consider a noncommutative version of the Davey-Stewartson equations and derive two families of quasideterminant solution via Darboux and binary Darboux transformations. These so…