  New finite energy traveling wave solutions with small speed are constructed
for the three dimensional Gross-Pitaevskii equation
  \begin{equation*} i\Psi_t= \Delta \Psi+(1-|\Psi|^2)\Psi,
  \end{equation*} where $\Psi$ is a complex valued function defined on
${\mathbb R}^3\times{\mathbb R}$. These solutions have the shape of $2n+1$
vortex rings, far away from each other. Among these vortex rings, $n+1$ of them
have positive orientation and the other $n$ of them have negative orientation.
The location of these rings are described by the roots of a sequence of
polynomials with rational coefficients. The polynomials found here can be
regarded as a generalization of the classical Adler-Moser polynomials and can
be expressed as the Wronskian of certain very special functions. The techniques
used in the derivation of these polynomials should have independent interest.
