Abstract:
Wave propagation in complex media with microstructure is currently receiving a great amount of attention. One approach to modeling such a medium is to assume that each point of the continuum is coupled to a number of oscillators (linearly or nonlinearly). The notion of ``fuzzy structure,'' currently popular in Western literature, can also be used to describe such media. Some simple examples of structures coupled to oscillators with different parameter distributions are described. The resonant dispersion equation (RDE) is derived and its stationary solutions of different types (including solitonlike solutions) are obtained and analyzed. Generalizations to elastic media with fractures are discussed [S. A. Rybak and Yu. I. Skrynnikov, ``Nonlinear Waves in Resonant Dispersion Media,'' in Nonlinear World, Proceedings of IV Intl. Workshop (World Scientific, 1989), pp. 664--670] [V. N. Alekseev and S. A. Rybak, ``Propagation of Stationary Sound Waves in Media with Bubbles,'' Acoust. Phys. 41(5), 690--698 (1995)].