Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 2 (2006), 032, 6 pages      nlin.SI/0603009      https://doi.org/10.3842/SIGMA.2006.032

Localized Induction Equation for Stretched Vortex Filament

Kimiaki Konno a and Hiroshi Kakuhata b
a) Department of Physics, College of Science and Technology, Nihon University, Tokyo 101-8308, Japan
b) Toyama University, Toyama 930-8555, Japan

Received October 05, 2005, in final form February 16, 2006; Published online March 02, 2006

Abstract
We study numerically the motion of the stretched vortex filaments by using the localized induction equation with the stretch and that without the stretch.

Key words: localized induction equation; stretch; vortex filament.

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References

  1. Konno K., Kakuhata H., A new type of stretched solutions excited by initially stretched vortex filaments for the local induction equation, Theor. Math. Phys., 2005, V.144, 1181-1189.
  2. Arms R.J., Hama F.R., Localized-induction concept on a curved vortex and motion of an elliptic vortex ring, Phys. Fluids, 1965, V.8, 553-559.
  3. Konno K., Kakuhata H., Stretching of vortex filament with corrections, in Nonlinear Physics: Theory and Experiment, II (2002, Gallipoli), River Edge, NJ, World Scientific Publishing, 2003, 273-279.
  4. Hashimoto H., A soliton on a vortex filament, J. Fluid Mech., 1972, V.51, 477-485.
  5. Konno K., Kakuhata H., A hierarchy for integrable equations of stretched vortex filament, J. Phys. Soc. Japan, 2005, V.74, 1427-1430.
  6. Konno K., Mitsuhashi T., Ichikawa Y.H., Dynamical processes of the dressed ion acoustic solitons, J. Phys. Soc. Japan, 1977, V.43, 669-674.

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