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Ultradiscrete kinks with supersonic speed in a layered crystal with realistic potentials

We develop a dynamical model of the propagating nonlinear localized excitations, supersonic kinks, in the cation layer in a silicate mica crystal. We start from purely electrostatic Coulomb interaction and add the Ziegler-Biersack-Littmark short-range repulsive potential and the periodic potential produced by other atoms of the lattice. This approach allows the construction of supersonic kinks which can propagate in the lattice within a large range of energies and velocities. The interparticle distances in the lattice kinks with high energy are physically reasonable values. The introduction of the periodic lattice potential results in the important feature that the kinks propagate with a single velocity and a single energy which are independent on the excitation conditions. The found kinks are ultra-discrete and can be described with the "magic wave number" $q\simeq 2π/3a$, which was previously revealed in the nonlinear sinusoidal waves and supersonic kinks in the Fermi-Pasta-Ulam lattice. The extreme discreteness of the supersonic kinks, with basically two particles moving at the same time, allows the interpretation of their double-kink structure. The energy of the supersonic kinks is between the possible source of $^{40}$K recoil in beta decay and the energy necessary for the ejection of an atom at the border as has been found experimentally.