Solitary Waves in Flexible, Arbitrary Elastic Helix

Abstract

The traveling solitary wave was recently discovered to be a very stable object existing in an inextensible, flexible helical fiber. In the present work, a flexible helical fiber with an arbitrary stress-strain relation is considered, and a general, analytical, steady-state solution of the 3D nonlinear vector equation is found. This solution describes a new class of spatial motion of an elastic string, which is shown to be a waveguide for subsonic solitary waves. The results confirm that the known solution for an inextensible fiber is a low-velocity or low-energy asymptote of the solution presented here. Another type of asymptotic solution derived here corresponds to a high-energy wave. In this case, when the amplitude of the wave increases, the wave speed and energy tend to infinity, and the effective wavelength tends to zero.