  Using a remarkable mapping from the original (3+1)dimensional Skyrme model to
the Sine-Gordon model, we construct the first analytic examples of Skyrmions as
well as of Skyrmions--anti-Skyrmions bound states within a finite box in 3+1
dimensional flat space-time. An analytic upper bound on the number of these
Skyrmions--anti-Skyrmions bound states is derived. We compute the critical
isospin chemical potential beyond which these Skyrmions cease to exist. With
these tools, we also construct topologically protected time-crystals:
time-periodic configurations whose time-dependence is protected by their
non-trivial winding number. These are striking realizations of the ideas of
Shapere and Wilczek. The critical isospin chemical potential for these
time-crystals is determined.
