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

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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: math
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: supr-con