Conformal Yang-Baxter equation on $\mathrm{C}\mathrm{u}\mathrm{r}({\mathrm{s}\mathrm{l}}_2(\mathbb{C}))$

In 2008, J. Liberati defined what is a conformal Lie bialgebra and introduced the conformal classical Yang-Baxter equation (CCYBE). An $L$-invariant solution to the weak version of CCYBE provides a conformal Lie bialgebra structure. We describe all solutions to the conformal classical Yang-Baxter equation on the current Lie conformal algebra $\mathrm{C}\mathrm{u}\mathrm{r}({\mathrm{s}\mathrm{l}}_2(\mathbb{C}))$ and to the weak version of it.