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Abstract and Applied Analysis
Volume 2014, Article ID 348920, 7 pages
Research Article

Strongly Nonlinear Transverse Perturbations in Phononic Crystals

1Radiophysics Department, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia
2Department of Nonlinear Geophysical Processes, Institute of Applied Physics, Nizhny Novgorod 603950, Russia
3Department of Applied Mathematics, Nizhny Novgorod Technical University, Nizhny Novgorod 603950, Russia

Received 7 March 2014; Accepted 3 June 2014; Published 2 July 2014

Academic Editor: Gani Stamov

Copyright © 2014 S. Nikitenkova and E. Pelinovsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The dynamics of the surface heterogeneities formation in low-dimensional phononic crystals is studied. It is shown that phononic transverse perturbations in this medium are highly nonlinear. They can be described with the help of the Riemann wave and may form stable wave structures of the finite amplitude. The Riemann wave deformation is described analytically. The Riemann wave time existence up to the beginning of the gradient catastrophe is calculated.