15 citations · 33 across the 11 of their papers we have counts for
11 papers
Elliptic solutions of the lattice CKP equation and its elliptic direct linearisation scheme
Ying-ying Sun, Da-jun Zhang, Frank Nijhoff
A direct linearisation scheme, based on an elliptic Cauchy kernel, is set up for the lattice CKP equation. This leads to an elliptic parametrisation of the lattice CKP equation, to…
The direct linearization scheme with the Lamé function: The KP equation and reductions
Xing Li, Ying-ying Sun, Da-jun Zhang
The paper starts from establishing an elliptic direct linearization (DL) scheme for the Kadomtsev-Petviashvili equation. The scheme consists of an integral equation (involving the…
Quasi-Periodic solutions of Two Dimensional Completely Resonant Reversible Schrödinger d Systems
Yingnan Sun, Shuaishuai Xue
We introduce an abstract KAM (Kolmogorov-Arnold-Moser) theorem for infinite dimensional reversible Schrödinger systems. Using this KAM theorem together with partial Birkhoff normal…
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…
Symmetric discrete AKP and BKP equations
Shangshuai Li, Frank W. Nijhoff, Ying-ying Sun +1
We show that when KP (Kadomtsev-Petviashvili) functions allow special symmetries, the discrete BKP equation can be expressed as a linear combination of the discrete AKP equatio…
Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity
Frank W Nijhoff, Ying-ying Sun, Da-jun Zhang
We establish an infinite family of solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the soluti…
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…
The Sylvester equation and the elliptic Korteweg-de Vries system
Ying-ying Sun, Da-jun Zhang, Frank W. Nijhoff
The elliptic Korteweg-de Vries (KdV) system is a multi-component generalization of the lattice potential KdV equation, whose soliton solutions are associated with an elliptic Cauch…
Solutions to the complex Korteweg-de Vries equation: Blow-up solutions and non-singular solutions
Ying-ying Sun, Juan-ming Yuan, Da-jun Zhang
In the paper two kinds of solutions are derived for the complex Korteweg-de Vries equation, including blow-up solutions and non-singular solutions. We derive blow-up solutions from…
Deriving conservation laws for ABS lattice equations from Lax pairs
Da-jun Zhang, Jun-wei Cheng, Ying-ying Sun
In the paper we derive infinitely many conservation laws for the ABS lattice equations from their Lax pairs. These conservation laws can algebraically be expressed by means of some…
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…