8 citations · 20 across the 7 of their papers we have counts for
5 papers · 1 filter
On the Lattice Potential KP Equation
Cewen Cao, Xiaoxue Xu, Da-jun Zhang
The paper presents an approach to derive finite genus solutions to the lattice potential Kadomtsev-Petviashvili (lpKP) equation introduced by F.W. Nijhoff, et al. This equation is…
A Gromov Hyperbolic metric and Möbius transformations
Xiaoxue Xu, Gendi Wang, Xiaohui Zhang
We compare a Gromov hyperbolic metric with the hyperbolic metric in the unit ball or in the upper half space, and prove sharp comparison inequalities between the Gromov hyperbolic…
Algebro-geometric integration of the Q1 lattice equation via nonlinear integrable symplectic maps
Xiaoxue Xu, Cewen Cao, Frank W Nijhoff
The Q1 lattice equation, a member in the Adler-Bobenko-Suris list of 3D consistent lattices, is investigated. By using the multidimensional consistency, a novel Lax pair for Q1 equ…
Finite genus solutions to the lattice Schwarzian Korteweg-de Vries equation
Xiaoxue Xu, Cewen Cao, Guangyao Zhang
Based on integrable Hamiltonian systems related to the derivative Schwarzian Korteweg-de Vries (SKdV) equation, a novel discrete Lax pair for the lattice SKdV (lSKdV) equation is g…
Integrable symplectic maps associated with discrete Korteweg-de Vries-type equations
Xiaoxue Xu, Mengmeng Jiang, Frank W Nijhoff
In this paper we present novel integrable symplectic maps, associated with ordinary difference equations, and show how they determine, in a remarkably diverse manner, the integrabi…