Exact solutions of nonlinear dynamical equations for large-amplitude atomic vibrations in arbitrary monoatomic chains with fixed ends
نویسندگان
چکیده
Intermode interactions in one-dimensional nonlinear periodic structures have been studied by many authors, starting with the classical work Fermi, Pasta, Ulam, and Tsingou (FPUT) middle of last century. However, symmetry selection rules for energy transfer between vibrational modes different symmetry, which lead to possibility excitation some bushes such modes, were not revealed. Each bush determines an exact solution dynamical equations considered system. The collection a given does change time, while there is continuous exchange these modes. Bushes normal (NNMs) are constructed aid group-theoretical methods therefore they can exist case large amplitude atomic vibrations any type interatomic interactions. In most publications, NNMs or similar objects systems investigated under boundary conditions. this paper, we present detailed study monoatomic chains fixed conditions, sheds light on series new properties intermode systems. We prove theorems that justify method constructing continuation conventional oscillations. Our was carried out FPUT chains, Lennard-Jones potential, as well carbon (carbynes) framework density functional theory. For (Rosenberg modes), amplitude–frequency diagrams presented their modulational instability briefly discussed. also argue favor fact our main results valid chain.
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ژورنال
عنوان ژورنال: Communications in Nonlinear Science and Numerical Simulation
سال: 2023
ISSN: ['1878-7274', '1007-5704']
DOI: https://doi.org/10.1016/j.cnsns.2023.107176