Nonradial entire solutions for Liouville systems

We consider the following system of Liouville equations:{−Δu1=2eu1+μeu2in R2−Δu2=μeu1+2eu2in R2∫R2eu1<+∞,∫R2eu2<+∞. We show the existence of at least n−[n3] global branches of nonradial solutions bifurcating from u1(x)=u2(x)=U(x)=log⁡64(2+μ)(8+|x|2)2 at the values μ=−2n2+n−2n2+n+2 for any n∈N.