Gianni Arioli, Hans Koch
Families of periodic solutions for some Hamiltonian PDEs
(1077K, pdf)

ABSTRACT.  We consider the nonlinear wave equation $u_{tt}-u_{xx}=\pm u^3$ 
and the beam equation $u_{tt}+u_{xxxx}=\pm u^3$ 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".