Longitudinal strain solitary waves in presence of cubic non-linearity

A new governing equation with combined quadratic and cubic non-linearities is obtained to account for longitudinal strain solitary waves in an elastic rod. It is shown that a strain solitary wave solution of this equation arises as a result of balance between quadratic non-linearity and dispersion and exists even in the absence of cubic non-linearity. However, the amplitude, the width and the velocity of the wave are affected by the cubic non-linearity causing, in particular, a narrowing of the wave. This allows to agree better with experiments on strain solitary wave generation.