8 citations · 20 across the 7 of their papers we have counts for
7 papers
Algebro-geometric solutions to the lattice potential modified Kadomtsev--Petviashvili equation
Xiaoxue Xu, Cewen Cao, Da-jun Zhang
Algebro-geometric solutions of the lattice potential modified Kadomtsev-Petviashvili (lpmKP) equation are constructed. A Darboux transformation of the Kaup--Newell spectral problem…
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…
Remarks on the scale invariant Cassinian metric
Gendi Wang, Xiaoxue Xu, Matti Vuorinen
We study the geometry of the scale invariant Cassinian metric and prove sharp comparison inequalities between this metric and the hyperbolic metric in the case when the domain is e…