5 citations · 26 across the 21 of their papers we have counts for
21 papers
Discrete Gerdjikov-Ivanov models and their higher-order counterparts from the Cauchy matrix scheme
Xiao-gang Mu, Song-lin Zhao
The Gerdjikov-Ivanov (GI) equation is an important model in the derivative nonlinear Schrodinger system, yet its fully discrete integrable analogues remain unexplored. In this pape…
Discretization of the Mikhailov model
Song-lin Zhao, Xiao-gang Mu, Da-jun Zhang
In this paper the Mikhailov model is discretized by means of the Cauchy matrix approach. A pair of discrete Miura transformations are constructed. The discrete Mikhailov model is a…
Bilinear structures of the fourth-order lattice Gel'fand-Dikii equations
Song-lin Zhao, Han Wang, Da-jun Zhang
In this paper we derive bilinear forms and present their solutions in Casoratians for several fourth-order lattice Gel'fand-Dikii (lattice GD-4) equations. These equations were rec…
Bilinearization-reduction approach to the classical and nonlocal semi-discrete modified Korteweg-de Vries equations with nonzero backgrounds
Xiao Deng, Hongyang Chen, Song-Lin Zhao +1
Quasi double Casoratian solutions are derived for a bilinear system reformulated from the coupled semi-discrete modified Korteweg-de Vries equations with nonzero backgrounds. These…
Solutions of local and nonlocal discrete complex modified Korteweg-de Vries equations and continuum limits
Ya-Nan Hu, Shou-Feng Shen, Song-lin Zhao
Cauchy matrix approach for the discrete Ablowitz-Kaup-Newell-Segur equations is reconsidered, where two `proper' discrete Ablowitz-Kaup-Newell-Segur equations and two `unproper' di…
Discrete nonlinear Schrödinger type equations: Solutions and continuum limits
Song-lin Zhao, Xiao-hui Feng, Wei Feng
As local and nonlocal reductions of a discrete second-order Ablowitz-Kaup-Newell-Segur equation, two discrete nonlinear Schrödinger type equations are considered. Through the bilin…
Revisit to solutions for Adler-Bobenko-Suris lattice equations and lattice Boussinesq-type equations
Ke Yan, Ying-ying Sun, Song-lin Zhao
Solutions for all Adler-Bobenko-Suris equations excluding Q4 and several lattice Boussinesq-type equations are reconsidered by employing the Cauchy matrix approach. Through introdu…
Solutions and continuum limits to nonlocal discrete modified Korteweg de-Vries equations
Song-lin Zhao, Xiao-bo Xiang, Shou-feng Shen
In this paper, we take advantage of the bilinearization reduction method to consider the local and nonlocal reduction of a discrete Ablowitz-Kaup-Newell-Segur equation. Exact solut…
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…
On the Fourth-Order Lattice Gel'fand-Dikii Equations
Guesh Yfter Tela, Song-Lin Zhao, Da-Jun Zhang
The fourth-order lattice Gel'fand-Dikii equations in quadrilateral form are investigated. Utilizing the direct linearization approach, we present some equations of the extended lat…
Cauchy matrix solutions to some local and nonlocal complex equations
Hai-Jing Xu, Song-lin Zhao
In this paper, we develop a Cauchy matrix reduction technique that enables us to obtain solutions for the reduced local and nonlocal complex equations from the Cauchy matrix soluti…
Local and nonlocal complex discrete and semi-discrete sine-Gordon equations and solutions
Xiao-bo Xiang, Wei Feng, Song-lin Zhao
In this paper, local and nonlocal complex reduction of a discrete and a semi-discrete negative order Ablowitz-Kaup-Newell- Segur equations is studied. Cauchy matrix type solutions,…
Solutions to nonlocal nonisospectral (2+1)-dimensional breaking soliton equations
Hai-jing Xu, Wei Feng, Song-lin Zhao
Nonlocal reductions of a nonisospectral (2+1)-dimensional breaking soliton Ablowitz-Kaup-Newell-Segur equation are discussed on the base of double Wronskian reduction technique. Va…
Rational solutions for three semi-discrete modified Korteweg-de Vries type equations
Yingying Sun, Songlin Zhao
In this paper, we consider three semi-discrete modified Korteweg-de Vries type equations which are the nonlinear lumped self-dual network equation,the semi-discrete lattice potenti…
Rational solutions to the ABS list: Degenerating approach
Song-lin Zhao, Da-jun Zhang
In the paper we first construct rational solutions for the Nijhoff-Quispel-Capel (NQC) equation by means of bilinear method. These solutions can be transferred to those of Q3 e…
Generalized Cauchy matrix approach for non-autonomous discrete Kadomtsev-Petviashvili system
Songlin Zhao, Wei Feng, Shoufeng Shen +1
In this paper, we investigate the non-autonomous discrete Kadomtsev-Petviashvili (KP) system in terms of generalized Cauchy matrix approach. These equations include non-autonomous…
Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach
Song-lin Zhao, Shou-feng Shen, Wei Feng
By the Sylvester equation $\bL\bM-\bM\bK=\br\bs^{\st}$ together with an evolution equation set of $\br$ and $\bs$, generalized Cauchy matrix approach is established to investigate…
The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation
Dan-dan Xu, Da-jun Zhang, Songling Zhao
The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation $\boldsymbol{K} \boldsy…
Solutions to the modified Korteweg-de Vries equation
Da-jun Zhang, Song-lin Zhao, Ying-ying Sun +1
This is a continuation of Ref.[1](arXiv:nlin.SI/0603008). In the present paper we review solutions to the modified Korteweg-de Vries equation in terms of Wronskians. The Wronskian…
Solutions to the non-autonomous ABS lattice equations: Casoratians and bilinearization
Ying Shi, Da-jun Zhang, Song-lin Zhao
In the paper non-autonomous H1, H2, H3 and Q1 equations in the ABS list are bilinearized. Their solutions are derived in Casoratian form. We also list out some Casoratian s…
Direct Linearization of extended lattice BSQ systems
Da-jun Zhang, Song-lin Zhao, Frank W Nijhoff
The direct linearization structure is presented of a "mild" but significant generalization of the lattice BSQ system. Some of the equations in this system were recently discovered…