Symmetry of Kelvin-wave dynamics and the Kelvin-wave cascade in the T=0 superfluid turbulence

This article considers the implications of tilt symmetry (symmetry with respect to tilting of the coordinate axis with respect to which vortex motion is studied) in the nonlinear dynamics of Kelvin waves. The conclusion is that although the spectrum of a Kelvin wave is not tilt-invariant, this does not compromise the tilt invariance of the Kelvin-wave cascade that is currently being vigorously debated in the theory of superfluid turbulence. The article investigates the effect of strong kelvon interaction on the power-law exponent for the Kelvin-wave cascade and suggests a simple picture of the crossover from the classical Kolmogorov cascade to the quantum Kelvin-wave cascade, which does not encounter a mismatch of the energy distributions at the crossover and does not require a broad intermediate interval for realization of the crossover.