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. In addition to 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." Our proofs are computer-Assisted.
Families of periodic solutions for some hamiltonian PDEs
ARIOLI, GIANNI;
2017-01-01
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. In addition to 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." Our proofs are computer-Assisted.File in questo prodotto:
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