  We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov
(NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is
studied using the GH polynomials and then the Lax pair is found. In particulr,
when $N=3,4,5$, one can get the Gold-fish model. The smooth rational solutions
of the NV equation are also constructed via the extended Moutard transformation
and the GH polynomials. The asymptotic behavior is discussed and then the
smooth rational solution of the Liouville equation is obtained.
