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The article considers implications of tilt symmetry (symmetry with respect totilting of the coordinate axis with respect to which vortex motion is studied)in the non-linear dynamics of Kelvin waves. The conclusion is that although thespectrum of Kelvin wave is not tilt-invariant, this does not compromise tiltinvariance of the Kelvin-wave cascade vividly argued now in the theory ofsuperfluid turbulence. The article investigates the effect of strong kelvoninteraction on the power-law exponent for the Kelvin-wave cascade and suggestsa simple picture of the crossover from the classical Kolmogorov cascade to thequantum Kelvin-wave cascade, which does not encounter with mismatch of theenergy distributions at the crossover and does not require a broad intermediateinterval for realization of the crossover.

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