A new type of finite-amplitude traveling or standing wave with an exact sinusoidal form and a short commensurate wavelength is predicted to exist in lattices with cubic and/or quartic anharmonic potential between any arbitrary number of nearest and non-nearest neighbors. Fast traveling nonlinear sinusoidal waves (NSW) can generate sinusoidal lattice solitons. Superposition of two NSW or sinusoidal solitons propagating in opposite directions can result in the formation of an extended or a localized standing-wave eigenmode. New exact solutions for localized standing-wave structures are found within a rigorous discrete-lattice approach.

• Received 16 June 1993

DOI:https://doi.org/10.1103/PhysRevLett.71.2058