New Formula for the Eigenvectors of the Gaudin Model in the $sl(3)$ Case

We propose new formulas for eigenvectors of the Gaudin model in the $sl(3)$ case. The central point of the construction is the explicit form of some operator $P$, which is used for derivation of eigenvalues given by the formula
$$|w_1,w_2)=\sum \limits^{\infty}_{n=0} \frac{P^n}{n!} |w_1,w_2,0>,$$
where $w_1, w_2$ fulfil the standard well-know Bethe Ansatz equations.