Nonlinear elementary excitations in a monoatomic chain with second nearest neighbour anharmonic interaction

By using a multiple scales method, we study the lattice vibration of a monoatomic chain taking into account the nearest neighbour and the second next nearest neighbour harmonic and anharmonic interactions. It is shown that nonpropagating solitons exist in any position of the Brillouin zone. Compared with that of a soliton in monoatomic chains with only nearest-neighbour interactions, the group velocity at the centre of the Brillouin zone is enhanced but attenuates more rapidly. In addition, a new position of zero velocity for the soliton is found in the first Brillouin. Our results show that the amplitude of this kind of soliton increases and the location of the soliton with the largest amplitude is close to the centre of the Brillouin zone.