Nonclassical symmetries of the fourth-order nonlinear partial differential equation with dispersion and dissipation are obtained and are used as a basis for deriving new exact solutions that are invariant with respect to these symmetries. The equation describes the propagation of nonlinear long-wavelength longitudinal deformations in an elastic rod placed in an external dissipative medium, the waves at the surface of a viscous liquid, etc. The solutions describing running waves are investigated based on the classical symmetries of areduced version of the basic equation. It is shown that such solutions can be constructed within the class of elliptic functions.
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