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A locally induced homoclinic motion of a vortex filament

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Abstract

An exact homoclinic solution of the Da Rios–Betchov equation is derived using the Hirota bilinear equation. This solution describes unsteady motions of a linearly unstable helical or wound closed filament under the localized induction approximation.

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References

  1. Akhmedieva N.N., Eleonskii V.M., Kulagin N.E.: Generation of periodic trains of picosecond pulses in an optical fiber: exact results. Sov. Phys. JETP 62, 894–899 (1985)

    Google Scholar 

  2. Ablowitz M.J., Herbst B.M.: On homoclinic structure and numerically induced chaos for the nonlinear Schrödinger equation. SIAM J. Appl. Math. 50, 339–351 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  3. Ricca R.L.: The contributioons of Da Rios and Levi-Civita to asymptotic potential theory and vortex filament dynamics. Fluid Dyn. Res 18, 245–268 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Hasimoto H.: A soliton on a vortex filament. J. Fluid Mech. 51, 477–485 (1972)

    Article  MATH  Google Scholar 

  5. Hirota R.: Bilinearlization of soliton equations. J. Phys Soc. Jpn. 51, 323–331 (1982)

    Article  MathSciNet  Google Scholar 

  6. Fukumoto Y., Miyazaki T.: N-solitons on a curved vortex filament. J. Phys. Soc. Jpn. 55, 4152–4155 (1986)

    Article  Google Scholar 

  7. Umeki M.: Complexification of wave numbers in solitons. Phys. Lett. A 236, 69–72 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  8. Stahlhofen A.A., Druxes H.: Comment on Complexification of wave numbers in solitons by M. Umeki. Phys. Lett. A 253, 247–248 (1999)

    Article  Google Scholar 

  9. Kida S.: A vortex filament moving without change of form. J. Fluid Mech. 112, 397–409 (1981)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ricca R.L.: Torus knots and polynomial invariants for a class of soliton equations. Chaos 3, 83–91 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  11. Ricca R.L.: Erratum: Torus knots and polynomial invariants for a class of soliton equations. Chaos 3, 83–91 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  12. Ricca R.L.: Erratum: Torus knots and polynomial invariants for a class of soliton equations. Chaos 5, 346 (1995)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan

    Makoto Umeki

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  1. Makoto Umeki
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Correspondence to Makoto Umeki.

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Communicated by H. Aref

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Umeki, M. A locally induced homoclinic motion of a vortex filament. Theor. Comput. Fluid Dyn. 24, 383–387 (2010). https://doi.org/10.1007/s00162-009-0160-3

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  • DOI: https://doi.org/10.1007/s00162-009-0160-3

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