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The existence of traveling and standing waves is investigated for chains ofcoupled pendula with periodic boundary conditions. The results are proven byapplying topological methods to subspaces of symmetric solutions. The mainadvantage of this approach comes from the fact that only properties of thelinearized forces are required. This allows to cover a wide range of modelssuch as Newton's cradle, the Fermi-Pasta-Ulam lattice and the Toda lattice.

Traveling and standing waves in coupled pendula and Newton's cradle