Intrinsically localized modes of bilinear FPU chains: Analytical study.

• Analytical approximation for DBs of infinitely long, bi-linear FPU chain is obtained • Zones of existence of ILMs in finite chains have been established analytically • Exact analytical solutions for ILMs emerging in finite chains are derived • Stability properties of ILM solutions of finite chains are established using the Fillipov method Present study concerns the analysis of stationary intrinsically localized modes emerging in bilinear and symmetric Fermi–Pasta–Ulam chains. Each element of the chain is coupled to its nearest neighbors through identical and symmetric (tension/compression) bilinear springs. The intrinsically localized modes are the time-periodic, localized vibration states which are manifested by the extreme energy localization on one and two bonds of the chain for bond - centered and site - centered symmetries, respectively. Approximate and exact analytical solutions of intrinsic localized modes are derived for the infinite as well as the finite chains, correspondingly. The derived analytical approximations allow to describe explicitly the amplitude wave profiles of these special localized states as well as to establish their zones of existence in the space of system parameters. In the second part of the study, we derive the exact analytical solutions for the same type of site- and bond- centered intrinsically localized modes supported by the finite bilinear Fermi–Pasta–Ulam chains and analyze their stability properties using Fillipov method. [ABSTRACT FROM AUTHOR]