Quasi-classical approximation in vortex filament dynamics. Integrable systems, gradient catastrophe and flutter

摘要: Quasiclassical approximation in the intrinsic description of vortex filament dynamics is discussed. Within this governing equations are given by elliptic system quasi-linear PDEs first order. Dispersionless Da Rios and dispersionless Hirota equation among them. They describe motion with slow varying curvature torsion without or axial flow. Gradient catastrophe for studied. It shown that geometrically manifests as a fast oscillation curve around rectifying plane which resembles flutter airfoils. Analytically it umbilic singularity terminology theory. demonstrated its double scaling regularization governed Painleve' I equation.