Nanoptera in Kelvin Lattices

The Kelvin lattice is a fundamental model to study the dynamical properties of metamaterials. This paper is devoted to quantitatively characterizing a nanopteron solution, which is a superposition of a central solitary wave and trailing oscillations, in a Kelvin lattice. We have illustrated that each nanopteron solution possesses a Stokes curve. We have also shown that the appearance of trailing oscillations in nanopteron solutions is a result of Stokes phenomena, which emerges when the Stokes curve is crossed in the complex plane. By employing an exponential asymptotic analysis, we have obtained analytically the relation between the amplitude of the trailing oscillations and the system parameters. Our theoretical predictions show good agreement with numerical simulations for a wide range of system parameters.