By means of the semidiscrete multiple-scale method, we study the existence and properties of high-order envelope solitons and discrete breathers in a homogeneous DNA chain model that is based on pairing enthalpies and site-dependent finite stacking. We obtain the analytical solutions for an envelope soliton, and find that at the Brillouin zone center, discrete breather solutions can appear below the bottom of the phonon band. The behavior of two solitons in collisions and the stability of discrete breathers are confirmed by numerical simulations of the exact equations of the system.
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.
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