Nonlinear waves in diatomic crystals |
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Authors: | AV Porubov IV Andrianov |
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Institution: | 1. Institute of Problems in Mechanical Engineering, Bolshoy av. 61, V.O., Saint-Petersburg 199178, Russia;2. Institute of General Mechanics, RWTH Aachen University, Templergraben 64, Aachen D-52062, Germany |
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Abstract: | A possible improvement of a continuum model for diatomic crystals is examined using continuum limit of a discrete diatomic model. For this purpose, various discrete models of diatomic lattice are compared at the linearized and weakly nonlinear levels. The suitable numbering of the atoms in the lattice is found which is better adopted for continualization than the familiar pair numbering introducing two sub-lattices. The coupled governing partial nonlinear differential equations for longitudinal strain and relative distance between the atoms are obtained in the continuum limit that allows us to describe localization of the strains due to the presence of the atoms of two kinds. It is found, that the equations obtained possess two kinds of localized wave solutions, one related to the acoustical branch and the other one related to the optical branch. |
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Keywords: | Diatomic lattice Continuum limit Nonlinear equation Traveling wave solution Localized strain wave |
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