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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.
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Nakajima et al. (1978) studied this question.
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