4 citations · 12 across the 9 of their papers we have counts for
11 papers
On number and evenness of solutions of the Toda system on flat tori with non-critical parameters
Zhijie Chen, Chang-Shou Lin
We study the Toda system with singular sources \[ \begin{cases} Δu+2e^{u}-e^v=4π\sum_{k=0}^m n_{1,k}δ_{p_k}\quad\text{ on }\; E_τ,\\ Δv+2e^{v}-e^u=4π\sum_{k=0}^m n_{2,k}δ_{…
Proof of a conjecture of Dahmen and Beukers on counting integral Lamé equations with finite monodromy
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, we prove Dahmen and Beukers' conjecture that the number of integral Lamé equations with index modulo scalar equivalence with the monodromy group dihedral …
The geometry of generalized Lame equation, III: One-to-one of the Riemann-Hilbert correspondence
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, the third in a series, we continue to study the generalized Lamé equation H with the Darboux-Treibich-Verdier potential \begin{equation*} y^{\pr…
A necessary and sufficient condition for the Darboux-Treibich-Verdier potential with its spectrum contained in
Zhijie Chen, Erjuan Fu, Chang-Shou Lin
In this paper, we study the spectrum of the complex Hill operator in with the Darboux-Treibich-Verdier potential \[q(x;τ):=…
The geometry of generalized Lamé equation, II: Existence of pre-modular forms and application
Zhijie Chen, Ting-Jung Kuo, Chang-Shou Lin
In this paper, the second in a series, we continue to study the generalized Lamé equation with the Treibich-Verdier potential \begin{equation*} y^{\prime \prime }(z)=\bigg[ \sum_{k…
Sharp nonexistence results for curvature equations with four singular sources on rectangular tori
Zhijie Chen, Chang-Shou Lin
In this paper, we prove that there are no solutions for the curvature equation \[ Δu+e^{u}=8πnδ_{0}\text{ on }E_τ, \quad n\in\mathbb{N}, \] where is a flat rectangular torus…