Periodic traveling waves in nonlinear chains

The behavior of periodic traveling-wave solutions for three different nonlinear chains is studied. In all cases it is found that nontrivial solutions exist only for the sector of the frequency-wavenumber plane given by omega(k)greater than or equal to omega(harmonic)(k). There is a ''dispersion relation'' (understood here only as a functional relationship between frequency and wavenumbers) for each value of the average energy of the wave. In the case of the Fermi-Pasta-Ulam chain this result can be related, through scaling, with the existence of only one energy-independent dispersion curve for the harmonic chain. The limits of small amplitude and large wavelength are also explored, and used to implement different approximations to the traveling wave solution.