Nonlinear theory of localized and periodic waves in solids undergoing major rearrangements of their crystalline structure |
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Authors: | E L Aero A N Bulygin |
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Institution: | 1. Institute of Problems in Mechanical Engineering, 61 Bolshoy Pr., V.O., St. Petersburg, Russia
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Abstract: | This article analyses the propagation of nonlinear periodic and localized waves. It examines crystals whose lattice consists
of two periodic sub-lattices. Arbitrary large displacements of sub-lattices u are assumed. This theory takes into account the additional element of translational symmetry. The relative displacement in
a sub-lattice for one period (and even for a whole number of periods) does not alter the structure of the whole complex lattice.
This means that its energy does not vary under such a relatively rigid translation of sub-lattices and should represent the
periodic function of micro-displacement. The energy also depends on the gradients of macroscopic displacement describing alterations
in the elementary cells of a crystal. The variational equations of macro- and micro-displacements are shown to be a nonlinear
generalization of the well-known linear equations of acoustic and optical modes of Karman, Born, and Huang Kun. Exact solutions
to these equations are obtained in the one-dimensional case—localized and periodic. Criteria are established for their mutual
transmutations. |
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Keywords: | |
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