Exact Solution for Localized States of Nonlinear Waves in the Structured Anharmonic Media with Two Interfaces

We study analytically the localized states of nonlinear waves propagating in an anharmonic medium along a system of two coupled identical parallel plane thin layers (interfaces). We find the exact localized soliton solution in the case of attractive character of both interfaces and anharmonic medium outside them. It is demonstrated that the exact solution is governed by a single scaling variable describing the ratio between the interface distance and the soliton state localization length. We obtain the exact results for the total number of elementary excitations and the total energy of the system and demonstrate numerically a monotonous behavior of the reduced total amount of elementary excitations bound in the localized state as a function of the scaling variable characterizing the distance between the interfaces.