Symmetries of nonlinear vibrations in tetrahedral molecular configurations

Irina Berezovik; Carlos García-Azpeitia; Wieslaw Krawcewicz

doi:10.3934/dcdsb.2018261

Article Contents

2019, Volume 24, Issue 6: 2473-2491. Doi: 10.3934/dcdsb.2018261

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Symmetries of nonlinear vibrations in tetrahedral molecular configurations

1.
Department of Mathematical Sciences University of Texas at Dallas Richardson, 75080 USA
2.
Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, 04510 México DF, México
3.
Center for Applied Mathematics, Guangzhou University, Guangzhou, China

Received: August 31, 2017

Revised: March 31, 2018

Early access: October 2018

Published: June 2019

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Abstract

We study nonlinear vibrational modes of oscillations for tetrahedral configurations of particles. In the case of tetraphosphorus, the interaction of atoms is given by bond stretching and van der Waals forces. Using the equivariant gradient degree, we present a topological classification of the spatio-temporal symmetries of the periodic solutions with finite Weyl's group. This procedure describes all the symmetries of the nonlinear vibrations for general force fields.

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Mathematics Subject Classification: 37J45, 34C25, 37G40, 47H11, 70H33.

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Figure 1. Stationary solution to equation (2) with tetrahedral symmetries

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