Classification and analysis of $SU(n+1)$ Toda system

Using PDE method, we first give a complete classification of $SU(n+1)$ Toda system with single source. Then we discuss applications of this classification result, including construction of the non-topological solutions of $A_2, B_2, G_2$ Chern–Simons–Higgs system, fully/partially blow-up analysis, and degree-counting formula for mean field Toda system.