Breather-induced quantised superfluid vortex filaments and their characterisation

Abstract

We study and characterise the breather-induced quantised superfluid vortex filaments which correspond to the Kuznetsov-Ma breather and super-regular breather excitations developing from localised perturbations. Such vortex filaments, emerging from an otherwise perturbed helical vortex, exhibit intriguing loop structures corresponding to the large amplitude of breathers due to the dual action of bending and twisting of the vortex. The loop induced by the Kuznetsov-Ma breather emerges periodically as time increases, while the loop structure triggered by the super-regular breather—the loop pair—exhibits striking symmetry breaking due to the broken reflection symmetry of the group velocities of the super-regular breather. In particular, we identify explicitly the generation conditions of these loop excitations by introducing a physical quantity—the integral of the relative quadratic curvature—which corresponds to the effective energy of breathers. Despite the nature of nonlinearity, it is demonstrated that this physical quantity shows a linear correlation with the loop size. These results will deepen our understanding of breather-induced vortex filaments and be helpful for controllable ring-like excitations on the vortices.

M-breather, M-lump, breather molecules and their interaction solutions for a (2+1)-dimensional KdV equation

“…Breather waves are oscillating solitary waves which are partially localized and have a periodic structure in space or time. Breather plays important roles in nonlinear physics and has been observed in many physical areas such as optics, hydrodynamics and quantized superfluid [43][44][45][46][47][48][49]. Lumps are two-dimensional solitons which decay algebraically in all directions [50,51].…”