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<p>In this paper, we study wave trains (periodic traveling waves) in a damped diatomic Fermi–Pasta–Ulam (FPU) lattice driven by external periodic forces. By applying nonlinear functional analysis, we show the existence and uniqueness of two different periodic waveform functions corresponding to light and heavy particles, respectively. In the case of small forcing and damping, Lyapunov–Schmidt reduction is employed to study the bifurcation of wave trains and the asymptotic expressions of the bifurcating solutions. For monatomic lattices, we adopt a nonstandard assumption of two waveform functions for adjacent particles, which results in two dispersion branches. This differs from traditional models using only one waveform function, where merely a single branch exists. Using this framework, we obtain new conclusions on the bifurcation of small-amplitude traveling waves.</p>

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Wave Trains in Forced–Damped Diatomic FPU Lattices

  • 期刊论文

  • 发表日期：

    2026年7月17日

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  • Ling Zhang,
  • Shangjiang Guo

摘要

In this paper, we study wave trains (periodic traveling waves) in a damped diatomic Fermi–Pasta–Ulam (FPU) lattice driven by external periodic forces. By applying nonlinear functional analysis, we show the existence and uniqueness of two different periodic waveform functions corresponding to light and heavy particles, respectively. In the case of small forcing and damping, Lyapunov–Schmidt reduction is employed to study the bifurcation of wave trains and the asymptotic expressions of the bifurcating solutions. For monatomic lattices, we adopt a nonstandard assumption of two waveform functions for adjacent particles, which results in two dispersion branches. This differs from traditional models using only one waveform function, where merely a single branch exists. Using this framework, we obtain new conclusions on the bifurcation of small-amplitude traveling waves.