Localized induction equation for stretched vortex filament (Q2495185)

The authors deal with a motion of the stretched vortex filaments where the filaments are described by the localized induction equation (shortly LIE). The LIE is given by \[ \vec X_t=\vec X_s\times\vec X_{ss}, \tag{1} \] where \(\vec X\) is the position vector \((X,Y,Z)\), \(s\) is the arclength and \(t\) is the time. This LIE was derived via approximation from \[ \vec X_t=\frac{\vec X_s\times\vec X_{ss}}{|\vec X_s|^3}\tag{2} \] In the present study the authors compare (2) with (1) in order to try to solve an initial value problem with the same initial vortex filaments.