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We derive a type of kinetic equation for Kelvin waves on quantized vortex filaments with random large-scale curvature, that describes step-by-step (local) energy cascade over scales caused by 4-wave interactions. Resulting new energy spectrum $ESb{LN}(k)propto k^{-5/3}$ must replace in future theory (e.g. in finding the quantum turbulence decay rate) the previously used spectrum $ESb {KS}(k)propto k^{-7/5}$, which was recently shown to be inconsistent due to nonlocality of the 6-wave energy cascade.
We study two different types of simplified models for Kelvin wave turbulence on quantized vortex lines in superfluids near zero temperature. Our first model is obtained from a truncated expansion of the Local Induction Approximation (Truncated-LIA) a
E.V. Kozik and B.V. Svistunov (KS) paper Symmetries and Interaction Coefficients of Kelvin waves, arXiv:1006.1789v1, [cond-mat.other] 9 Jun 2010, contains a comment on paper Symmetries and Interaction coefficients of Kelvin waves, V. V. Lebedev and V
In wave turbulence, it has been believed that statistical properties are well described by the weak turbulence theory, in which nonlinear interactions among wavenumbers are assumed to be small. In the weak turbulence theory, separation of linear and
Both the Kelvin wave and the Kolmogorov turbulence interpretations presented in the PRL, [v. 103, 084501 (2009) by J. Yepez, G. Vahala, L.Vahala and M. Soe, arXiv:0905.0159] are misleading, and much more theoretical analysis needs to be done for the
A single-wavenumber representation of nonlinear energy spectrum, i.e., stretching energy spectrum is found in elastic-wave turbulence governed by the Foppl-von Karman (FvK) equation. The representation enables energy decomposition analysis in the wav