Existence and modulation of traveling waves in particle chains.

摘要

We consider a one-dimensional particle chain whose dynamics are governed by the following system of differential equations;We present two proofs, one based on a variational principle and the other on topological methods, in particular, degree theory.;For small-amplitude waves, based on perturbation techniques, we describe the form of the travelling waves, and we derive the near-linear dispersion relation. For the fully nonlinear case, when the amplitude of the waves is high, we use numerical methods to compute the travelling wave solution and the nonlinear dispersion relation.;It is well-known (see (HFM), (VDO), (Kamv)) that, in the special case of Toda interaction potential