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.
S. Nikitenkova. E. Pelinovsky. "Strongly Nonlinear Transverse Perturbations in Phononic Crystals." Abstr. Appl. Anal. 2014 (SI70) 1 - 7, 2014. https://doi.org/10.1155/2014/348920