Strongly nonlinear waves – A new trend of nonlinear acoustics

Abstract

Strongly nonlinear waves (SNWs) and extreme states of matter are key physical concepts. A SNW is a wave whose amplitude is on the order of the material's internal strength. High-intensity light is a weak nonlinear wave (WNW) if its electric field is weaker than the intra-atomic: E ≪ 1011 V/m. A SNW irreversibly modifies a medium, up to its destruction. In vacuum a wave 1018 V/m is strong, when it creates electron-positron pairs. In acoustics SNWs must be distinguished from WNWs which also can display strongly nonlinear phenomena. When a shock front appears at a distance of 102−103 wavelengths in water, nonlinearity is weak but strongly expressed. The acoustic pressure is 105−106 Pa, much less than the internal pressure 2.2 × 109 Pa. However, impurities decrease the breaking strength, and waves create bubbles at smaller pressures. An explosive wave is also a SNW, breaking solids. Nuclear explosions may even create new chemical elements. For WNWs the equation of state can be expanded in power or functional series. However, these cannot be used in three cases. First, if the equation contains singularities, like for “clapping” and Hertz nonlinearities of heterogeneous solids. Second, if the series is divergent. Third, when the linear term is absent and the higher nonlinearities dominate. Such SNWs appear in mechanics and in quantum field theory. Mathematical models of SNW, solutions, and new phenomena observed experimentally will be presented.