29 citations · 55 across the 9 of their papers we have counts for
9 papers
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…
Solutions and continuum limits to nonlocal discrete sine-Gordon equations: bilinearization reduction method
Xiao-bo Xiang, Song-lin Zhao, Ying Shi
As with nonlocal continuous and semi-discrete integrable systems, the study of nonlocal discrete integrable systems is also of interest. In this paper, local and nonlocal reduction…
graded discrete integrable systems and Darboux transformations
Ying Shi
We present the Darboux transformations for a novel class of two-dimensional discrete integrable systems named as graded discrete integrable systems, which…
Binary Darboux transformations for discrete modified Boussinesq equation
Ying Shi, Junxiao Zhao
We obtain the well-known discrete modified Boussinesq equation in two-component form as well as its Lax pair in matrix form through a 3-periodic reduction technique on t…
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…
Spectrum transformation and conservation laws of the lattice potential KdV equation
Senyue Lou, Ying Shi, Da-jun Zhang
Many multi-dimensional consistent discrete systems have soliton solutions with nonzero backgrounds, which brings difficulty in the investigation of integrable characteristics. In t…