Delocalized Nonlinear Vibrational Modes of BCC Lattice

The article presents several exact solutions of the equations of motion of atoms in a BCC crystal, called delocalized nonlinear vibrational modes (DNVMs). The exact solutions are obtained by analyzing the BCC lattice point symmetry group only, therefore, they exist for any type of interatomic interactions and for any amplitudes. All studied DNVMs are vibrational modes with one degree of freedom. The dependence between frequency and amplitude of DNVMs is calculated using the Fermi-Pasta-Ulam potential with hard type nonlinearity when considering interatomic interactions up to the fourth neighbor. There are seven groups among the 34 studied DNVMs with the same frequency of vibrational modes in the small amplitude limit within each group. This fact is explained by some DNVMs being superpositions of others after applying point symmetry transformations. The obtained results can be to test the interatomic potentials of BCC crystals.