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.
Demontis, F., Ortenzi, G., Van Der Mee, C. (2015). Exact solutions of the Hirota equation and vortex filaments motion. PHYSICA D-NONLINEAR PHENOMENA, 313, 61-80 [10.1016/j.physd.2015.09.009].
Exact solutions of the Hirota equation and vortex filaments motion
ORTENZI, GIOVANNI
;
2015
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.
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