Strongly nonlinear phenomena in acoustics

The difference between strongly nonlinear waves and waves with strongly displayed weak nonlinearity is pointed out. The classification of strongly nonlinear systems is given. The simplest structural features of meta-materials having high nonlinearity are described. Examples of mathematical models having sufficient generality and interesting for nonlinear wave physics are given. Particle-like properties of singular solutions, as well as some unusual phenomena are pointed out. Accretion, self-trapping and self-splitting can exemplify such phenomena.