On number and evenness of solutions of the $SU(3)$ Toda system on flat tori with non-critical parameters

Zhijie Chen, Chang-Shou Lin

We study the $SU(3)$ 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_{…