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A novel, protean, topological soliton has recently been shown to emerge insystems of repulsive particles in cylindrical geometries, whose statics isdescribed by the number-theoretical objects of phyllotaxis. Here we present aminimal and local continuum model that can explain many of the features of thephyllotactic soliton, such as locked speed, screw shift, energy transport and,for Wigner crystal on a nanotube, charge transport. The treatment is generaland should apply to other spiraling systems. Unlike e.g. Sine-Gornon-likesystems, our solitons can exist between non-degenerate structure, imply a powerflow through the system, dynamics of the domains it separates; we also predictpulses, both static and dynamic. Applications include charge transport inWigner Crystals on nanotubes or A- to B-DNA transitions.

Spiraling Solitons: a Continuum Model for Dynamical Phyllotaxis and Beyond