Frequence spectrum of monochromatic vibrations of a one-dimensional nonlinear chain of finite length

The example of a one-dimensional elastic chain of finite length of the type of a system with frozen internal rotations is used to study the influence of nonlinearity on the spectrum of etgenvibrations of such a chain. It is shown that the nature of the possible single-particle vibrations depends essentially on the boundary conditions. For certain boundary conditions, one can have new branches whose frequencies lie in the forbidden zone of the harmonic spectrum. The deformation of the harmonic spectrum with increasing energy of the vibrations is analyzed.