4 papers
Geometric Algorithm of Schrödinger Flow on a Sphere
Hsiao-Fan Liu
We construct the solution to the periodic Cauchy problem of the Schrödinger flow on the sphere. Such construction of solutions is formulated explicitly and therefore a geometric al…
A q-generalization of the Toda equations for the q-Laguerre/Hermite orthogonal polynomials
Chuan-Tsung Chan, Hsiao-Fan Liu
Based on the motivation of generalizing the correspondence between the Lax equation for the Toda lattice and the deformation theory of the orthogonal polynomials, we derive a q-def…
Star Mean Curvature Flow on 3 manifolds and its Bäcklund Transformations
Hsiao-Fan Liu
The Hodge star mean curvature flow on a 3-dimensional Riemannian or pseudo-Riemannian manifold is a natural nonlinear dispersive curve flow in geometric analysis. A curve flow is i…
Graphic Enumerations and Discrete Painlevé Equations via Random Matrix Models
Chuan-Tsung Chan, Hsiao-Fan Liu
We revisit the enumeration problems of random discrete surfaces (RDS) based on solutions of the discrete equations derived from the matrix models. For RDS made of squares, the recu…