We consider an expansion of the strongly interacting superfluid Fermi gas in the vacuum in the so-called unitary regime when the chemical potential $\mu \propto \hbar^2n^{2/3}/m$ where $n$ is the density of the Bose-Einstein condensate of Cooper pairs of fermionic atoms. Such expansion can be described in the framework of the Gross-Pitaevskii equation (GPE) [1]. Because of the chemical potential dependence on the density $\sim n^{2/3}$ the GPE has additional symmetries resulting in existence of the virial theorem connected the mean size of the gas cloud and its Hamiltonian. It leads asymptotically at $t\to\infty$ to the ballistic expansion of the gas. We carefully study such asymptotics and reveal a perfect matching between the quasi-classical self-similar solution and the ballistic expansion of the non-interacting gas [2]. This matching is governed by the virial theorem derived in [3] utilizing the Talanov transformation [4] which was first obtained for the stationary self-focusing of light in the media with cubic nonlinearity due to the Kerr effect. In the quasi-classical limit the equations of motion coincide with 3D hydrodynamics for the perfect gas with $\gamma=5/3$ which, as it was demonstrated by S.I. Anisimov and Yu.I. Lysikov [5], have additional symmetry. Just this symmetry provides one to find self-similar solution which describes,
on the background of the gas expansion, the angular deformations of the gas shape in the framework of the Ermakov-Ray-Reid type system.

The work of E.K. was performed under support of the Russian Science Foundation (grant 19-72-30028).

\vspace{0.2 cm}
{\bf References}

\vspace{0.2 cm}


\noindent [1] L.P. Pitaevskii, Superfluid Fermi liquid in a unitary
regime, Physics Uspekhi, v.51, pp.603-608, 2008.

\noindent [2] E.A. Kuznetsov, M.Yu. Kagan and
A.V. Turlapov. Expansion of the strongly interacting superfluid Fermi gas:
symmetries and self-similar regimes, arXiv:1903.04245 2019,
Phys. Rev. A (submitted).

\noindent [3] E.A. Kuznetsov, S.K. Turitsyn, Talanov
transformation in self-focusing problems and instability of stationary
waveguides, Phys.Lett., v.112 A, pp. 273-276, 1985.

\noindent [4] V.I. Talanov, On the self-focusing of light in the cubic
media, Pis'ma Zh.Eksp.Teor.Fiz., v.11, p.303, 1970.

\noindent [5] S.I. Anisimov and Yu.I. Lysikov. Expansion of a gas cloud in vacuum,
Journal of Applied Mathematics and Mechanics, v. 34, pp. 882--885,
1970.