Solitons in a Diatomic Chain with Competing Nonlinearities

A one-dimensional diatomic chain whose energy contains cubic and quartic terms in the atomic displacements is considered. A modified asymptotic method is proposed for finding soliton solutions to equations describing systems with nonlinearities of various symmetry. It is shown that the dynamics of the model in question can be described in terms of equations that are similar to the dynamic equations for a diatomic chain with an even potential function. Soliton solutions of a new, unusual type are found in the specific case of a free diatomic chain with a purely cubic anharmonic potential.