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Integrable stationary solution for the fully nonlinear local induction equation describing the motion of a vortex filament

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Abstract

In this brief communication, we demonstrate an implicit exact stationary solution to the fully nonlinear local induction equation describing the motion of a vortex filament. The solution, which is periodic in the spatial variable, is governed by a second-order nonlinear equation that has two exact first integrals.

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References

  1. Shivamoggi B.K., van Heijst G.J.F.: Motion of a vortex filament in the local induction approximation: Reformulation of the Da Rios-Betchov equations in the extrinsic filament coordinate space. Phys. Lett. A 374, 1742 (2010)

    Article  MATH  Google Scholar 

  2. Dmitriyev V.P.: Helical waves on a vortex filament. Am. J. Phys. 73, 563 (2005)

    Article  Google Scholar 

  3. Van Gorder, R.A.: Motion of a vortex filament in the local induction approximation: a perturbative approach. Theor. Comput. Fluid Dyn. (2011, in press). doi:10.1007/s00162-010-0218-2

  4. Da Rios L.S.: Sul moto d’un liquido indefinite con un filetto vorticoso di forma qualunque. Rend. Circ. Mat. Palermo 22, 117 (1906)

    Article  MATH  Google Scholar 

  5. Arms R.J., Hama F.R.: Localized-induction concept on a curved vortex and motion of an elliptic vortex ring. Phys. Fluids 8, 553 (1965)

    Article  Google Scholar 

  6. Umeki M.: A locally induced homoclinic motion of a vortex filament. Theor. Comput. Fluid Dyn. 24, 383 (2010)

    Article  MATH  Google Scholar 

  7. Hasimoto H.: Motion of a Vortex Filament and its relation to Elastica. J. Phys. Soc. Jpn. 31, 293 (1971)

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Central Florida, Orlando, FL, 32816-1364, USA

    Robert A. Van Gorder

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  1. Robert A. Van Gorder
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Correspondence to Robert A. Van Gorder.

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Communicated by Hussaini.

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Van Gorder, R.A. Integrable stationary solution for the fully nonlinear local induction equation describing the motion of a vortex filament. Theor. Comput. Fluid Dyn. 26, 591–594 (2012). https://doi.org/10.1007/s00162-011-0244-8

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  • DOI: https://doi.org/10.1007/s00162-011-0244-8

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