New amplitude equations for thin elastic rods

The stability of twisted straight rods is described within the framework of the time dependent Kirchhoff equations for thin elastic; filaments. A perturbation method is developed to study the linear stability of this problem and find the dispersion relations. A nonlinear analysis results in a new amplitude equation, describing the deformation of the rod beyond the instability, which takes the form of a pair of nonlinear, second-order evolution equations coupling the local deformation amplitude to the twist density. Various solutions, Such as solitary waves, are presented.