Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2007-08-09
Nonlinear Sciences
Exactly Solvable and Integrable Systems
26 pages, 4 figures
Scientific paper
10.1143/PTP.119.701
We have constructed one-phase quasi-periodic solutions of the curve equation induced by the mKdV equation. The solution is expressed in terms of the elliptic functions of Weierstrass. This solution can describe curve dynamics such as a vortex filament with axial velocity embedded in an incompressible inviscid fluid. There exist two types of curves (type-A, type-B) according to the form of the main spectra of the finite-band integrated solution. Our solution includes various filament shapes such as the Kelvin-type wave, the rigid vortex, plane curves, closed curves, and the Hasimoto one-solitonic filament.
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