Periodic and localized solutions in chains of oscillators with softening or hardening cubic nonlinearity

Spatially periodic and stationary localized solutions arising from the dynamics of chains of linearly coupled mechanical oscillators characterized by on site cubic nonlinearity are addressed aiming to explore their relationship with the underlying nonlinear wave propagation regions. Softening and hardening nonlinearities are considered, and regions of occurrence of discrete breathers and multibreathers associated with homoclinic or heteroclinic connections are identified. © 2014 Springer Science+Business Media Dordrecht.