Nonlinear solitary waves in nonlocal elastic solids

Abstract

The possibility of new weakly nonlinear solitary waves in nonlocal elastic media is demonstrated. The properties of these waves are determined by the characteristic features of wave dispersion in the linear approximation, and their velocity and amplitude cannot exceed certain limiting values. In the case of small amplitudes and velocities close to the velocity of sound, the profile of the waves under consideration coincides with the profile of the soliton described by the Korteweg-de Vries equation. When the amplitude and velocity of the aforementioned waves reach their limiting values, the wave profile sharpens. It is concluded that the propagation of such waves in rocks and soils is possible.

Wave moment geodynamics

“…"The slow dynamics" and its impact on "the elastic properties of materials" are specified in [Korobov et al, 2013]. The idea of the new type of rotation waves [Vikulin, 2010[Vikulin, , 2011, as the consequence of the concept envisaging that the geomedium is composed of rotating blocks, is consistent with results of theoretical and instrumental acoustic studies of 'normal' solids [Korobov et al, 2013;Pamyatnykh, Ursulov, 2012;Rudenko et al, 2012].…”

“…The conclusion about the existence of "a new type of solitary waves" with "limiting velocity values" is also stated for non-local elastic solids [Pamyatnykh, Ursulov, 2012]. The idea of a 'slow' mode "propagating with a velocity that is much lower than the velocity of sound in liquids, solid granules and gas" is theoretically and experimentally supported by results of theoretical and experimental studies [Rudenko et al, 2012].…”