Exact solutions of the Hirota equation and vortex filaments motion

DEMONTIS, FRANCESCO;Ortenzi, G.

;VAN DER MEE, CORNELIS VICTOR MARIA

2015-01-01

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Abstract

By using the Inverse Scattering Transform we construct an explicit soliton solution formula for the Hirota equation. The formula obtained allows one to get, as a particular case, the N-soliton solution, the breather solution and, most relevantly, a new class of solutions called multipole soliton solutions. We use these exact solutions to study the motion of a vortex filament in an incompressible Euler fluid with nonzero axial velocity.