Get distribution from characteristic function

Question

I have $$\phi(t_1,t_2)=\frac{1}{3}e^{\{e^{-t_1^2-t_2^2}-1-t_1^2\}}+\frac{2}{3}e^{\{e^{-|t_1+t_2|}-1-t_2^2\}}$$ I see, that it is the convex combination of two distributions, but what is their distribution?