  We study the propagation of one-dimentional optical beams in a weakly
nonlocal medium exhibiting cubic-quintic nonlinearity. A nonlinear equation
governing the evolution of the beam intensity in the nonlocal medium is derived
thereby which allows us to examine whether the traveling-waves exist in such
optical material. An efficient transformation is applied to obtain explicit
solutions of the envelope model equation in the presence of all material
parameters. We find that a variety of periodic waves accompanied with a
nonlinear chirp do exist in the system in the presence of the weak nonlocality.
Chirped localized intensity dips on a continuous-wave background as well as
solitary waves of the bright and dark types are obtained in a long wave limit.
A class of propagating chirped self-similar solitary beams is also identified
in the material with the consideration of the inhomogeneities of media. The
applications of the obtained self-similar structures are discussed by
considering a periodic distributed amplification system.
