New solutions are found for the non-relativistic hydrodynamical equations.
These solutions describe expanding matter with a Gaussian density profile. In
the simplest case, thermal equilibrium is maintained without any interaction,
the energy is conserved, and the process is isentropic. More general solutions
are also obtained that describe explosions driven by heat production, or
contraction of the matter caused by energy loss.Comment: 6 pages, LaTeX. Submitted to Physics Letters B. Shortened from 9
pages, errors corrected in the "More general solutions" sectio
