Semiclassical intrinsic localized modes in the β-Fermi–Pasta–Ulam lattice model with first- and second-nearest neighbor interactions

Abstract

We present an analytical study on intrinsic localized modes (ILMs) in the quantum [Formula: see text]-Fermi–Pasta–Ulam lattice model with first- and second-nearest neighbor interactions by means of the semiclassical approach. We quantize the lattice model Hamiltonian by introducing vibron creation and annihilation operators, and retaining only number conserving terms. The coherent state representation is considered as the basic representation of the quantum lattice system. In order to obtain the ILM solutions, we adopt the multiple scales method combined with a quasidiscreteness approximation. It is found that, when the system parameters satisfy [Formula: see text], at the Brillouin zone (BZ) boundary, a bright ILM occurs above the top of the harmonic wave frequency band. While for [Formula: see text], our results indicate that at wave number [Formula: see text] a bright ILM occurs above the top of the harmonic wave frequency band and at the BZ boundary, the system support a dark intrinsic localized resonant mode.