Discrete Breathers in a Square Lattice Based on Delocalized Modes

Article Engineering, Mechanical

One-component delocalized nonlinear vibrational modes of square lattices

D. S. Ryabov et al.

Summary: This paper analyzes all possible one-component delocalized nonlinear vibrational modes (DNVMs) in a square lattice. The DNVMs are obtained solely based on the symmetry of the lattice, thus existing regardless of the particle interactions. The interactions between nearest and next nearest neighbors are described using the beta-FPUT potential. Frequency, kinetic and potential energies of each DNVM are described as functions of amplitude. The paper also presents mechanical stresses caused by DNVMs and the effect of DNVMs on the lattice's stiffness constants. DNVMs with higher vibration frequencies have a stronger impact on the lattice's mechanical properties. Analytical analysis of DNVMs is provided. It is discovered that two out of the sixteen one-component DNVMs can have frequencies above the phonon band across their entire amplitude range. These DNVMs can be used to construct discrete breathers by applying localizing functions. The modulational instability of these two DNVMs leads to the formation of chaotic DBs. The presented results contribute to a better understanding of the nonlinear dynamics of a square lattice by analyzing the properties of a class of delocalized exact solutions and demonstrating their connection with discrete breathers.

NONLINEAR DYNAMICS (2023)

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Article Physics, Fluids & Plasmas

Discrete breathers in a triangular β-Fermi-Pasta-Ulam-Tsingou lattice

Rita Babicheva et al.

Summary: The article proposes a practical approach to search for (quasi-) discrete breathers on a triangular beta-FPUT lattice by superimposing localizing functions on delocalized nonlinear vibrational modes with frequencies above the phonon spectrum of the lattice. It discusses zero-dimensional and one-dimensional breathers, with the latter divided into two families based on triangular lattice and chain vibrational modes. The systematic approach reveals various spatially localized oscillations bifurcating from the upper edge of the phonon band.

PHYSICAL REVIEW E (2021)

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Article Materials Science, Multidisciplinary