| Abstract: |
We consider the nonlinear wave equation
utt-uxx=±u3
and the beam equation
utt+uxxxx=±u3
on an interval.
Numerical observations indicate that time-periodic solutions
for these equations are organized into structures that resemble branches
and seem to undergo bifurcations.
Besides describing our observations,
we prove the existence of time-periodic solutions
for various periods (a set of positive measure
in the case of the beam equation)
along the main nontrivial "branch".
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