Analytical solutions to zeroth-order dispersion relations of a cylindrical metallic nanowire near the backbending pointL. Wan, Y.M. Huang, C.K. Dong and H.J. LuoEur. Phys. J. B, 85 1 (2012) 17DOI: https://doi.org/10.1140/epjb/e2011-20775-7