Solitons on a vortex filament with axial flow

Abstract

Studies of motion of a vortex filament provide the crucial problems of pure and mathematical physics. Here, the extended local induction equation, which accounts for the effect of axial flow, has been investigated on the basis of the inverse scattering method. The present analysis provides a two soliton solution with the intrinsic symmetry, while the solution constructed by the method of soliton surface does not show this property explicitly. The characteristics parameters of the vortex soliton are determined from the experimental observation of a solitary wave propagating along the vortex filament. Though the two soliton collision process is consistent with the experimental observation, our theoretical analysis is unable to account for the observed large phase jump after the head-on collision of two solitons. © 1992.