Title

Exact solution for the self-induced motion of a vortex filament in the arc-length representation of the local induction approximation

Authors

Authors

R. A. Van Gorder

Comments

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Abbreviated Journal Title

Phys. Rev. E

Keywords

SUPERFLUID-HELIUM; EQUATIONS; KNOTS; INVARIANTS; DYNAMICS; SOLITON; WAVES; HE-4; Physics, Fluids & Plasmas; Physics, Mathematical

Abstract

We review two formulations of the fully nonlinear local induction equation approximating the self-induced motion of the vortex filament (in the local induction approximation), corresponding to the Cartesian and arc-length coordinate systems. The arc-length representation put forth by Umeki [Theor. Comput. Fluid Dyn. 24, 383 (2010)] results in a type of 1 + 1 derivative nonlinear Schrodinger (NLS) equation describing the motion of such a vortex filament. We obtain exact stationary solutions to this derivative NLS equation; such exact solutions are a rarity. These solutions are periodic in space and we determine the nonlinear dependence of the period on the amplitude.

Journal Title

Physical Review E

Volume

86

Issue/Number

5

Publication Date

1-1-2012

Document Type

Article

Language

English

First Page

4

WOS Identifier

WOS:000310610300001

ISSN

1539-3755

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