STABILITY CONDITION AND DYNAMIC BEHAVIOR FOR ONE-DIMENSIONAL AND 2-DIMENSIONAL SOLITARY WAVES - STABILITY AND INTERACTION OF 2 VORTEX LINES IN SUPERFLUID-HELIUM

A general stability condition and the interactions of particlelike solutions of one-dimensional sine-Gordon-type nonlinear partial differential equations are studied by numerical calculations and with the potentials which are derived from these equations. The stability condition is extended to the two-dimensional case and is applied to the study of the stability of a single vortex state and two-vortex interactions in superfluid helium near the λ point. It was found by numerical calculations that two-vortex filaments of the same rotation repel each other, while those with opposite rotation attract each other and annihilate, contrary to classical theory. © 1978 The American Physical Society.