We study the spatiotemporal solitary modes that propagate in a hollow twistedcylinder waveguide pipe with a self-focusing Kerr nonlinearity. Three genericsolitary modes, one belonging to the zero-harmonic (0H) and the other twobelonging to the first-harmonic (1H), are found in the first rotationalBrillouin zone. The 0H solitary modes can be termed as a quasi-1D(one-dimensional) temporal soliton. Their characteristics depend only on theenergy flow. The 1H solitary mode can be termed a quasi-2D (two-dimensional)bullet, whose width is much narrower than the angular domain of the waveguide.In contrast to the 0H mode, the characteristics of the 1H solitary mode dependon both their energy flow and the rotating speed of the waveguide. Wedemonstrate numerically that the 1H solitary modes are stable when their energyflow is smaller than the threshold norm of the \emph{Townes soliton}. Theboundaries of the bistable area for these two types of solitary modes arepredicted by the analyses via two-mode approximation. This prediction is inaccordance with the numerical findings. We also demonstrate analytically thatthe 1H solitary mode of this system can be applied to emulate the nonlineardynamics of solitary modes with 1D Rashba spin-orbit (SO) coupling by optics.Two degenerated states of the 1H solitary mode, semi-dipole and mixed mode, arefound from this setting via the mechanism of SO coupling. Collisions betweenthe pair of these two types of solitary modes are also discussed in the paper.The pair of the 0H solitary mode features only the elastic collision, whereasthe pair of 1H solitary modes can feature both elastic and inelastic collisionwhen the total energy flow of the two modes are smaller or close to thethreshold norm of the \emph{Townes soliton}.
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