  We solve the Cauchy problem for the relativistic closed string in Minkowski
space $M^{3+1}$, including the cases where the initial data has a knot like
topology. We give the general conditions for the world sheet of a closed
knotted string to be a time periodic surface. In the particular case of zero
initial string velocity the period of the world sheet is proportional to half
the length ($\ell$) of the initial string and a knotted string always collapses
to a link for $t=\ell/4$. Relativistic closed strings are dynamically evolving
or pulsating structures in spacetime, and knotted or unknotted like structures
remain stable over time. The generation of arbitrary $n$-fold knots, starting
with an initial simple link configuration with non zero velocity is possible.
