Nonlinear solitary waves in nonlocal elastic solids

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.