Hamilton's equations of motion of a vortex filament in the rotating Bose-Einstein condensate and their "soliton" solutions

Abstract

The equation of motion of a quantized vortex filament in a trapped Bose-Einstein condensate [A. A. Svidzinsky and A. L. Fetter, Phys. Rev. A {\bf 62}, 063617 (2000)] has been generalized to the case of an arbitrary anharmonic anisotropic rotating trap and presented in a variational form. For condensate density profiles of the form $ρ=f(x^2+y^2+\mbox{Re\,}Ψ(x+iy))$ in the presence of the plane of symmetry $y=0$, the solutions $x(z)$ describing stationary vortices of U and S types coming to the surface and solitary waves have been found in quadratures. Analogous three-dimensional configurations of the vortex filament uniformly moving along the $z$ axis have also been found in strictly cylindrical geometry. The dependence of solutions on the form of the function $f(q)$ has been analyzed.

4 pages, 4 figures

References in corpus (1)

• Bending-wave Instability of a Vortex Ring in a Trapped Bose-Einstein Condensate

Cited by in corpus (2)

• Parametric instability of oscillations of a vortex ring in a $z$-periodic Bose-Einstein condensate and the recurrence to starting state
• Some exact solutions of the local induction equation for motion of a vortex in a Bose-Einstein condensate with Gaussian density profile