Nonlinear waves and solitons in models of fault block geological media

This is an overview of theoretical research on solitons and other nonlinear waves induced by deformation in fault block (fragmented) geological media, including a brief description of available models with their geophysical and geodynamic applications. The cited models correspond to the classical and perturbed sine-Gordon equations and use the rotation angle and displacement of fault blocks as dynamic variables. The models simulate kinematics and dynamics of traveling deformation fronts (kinks and solitons) generated in faulted rocks. The sine-Gordon equation is presented in its seismological and geomechanic applications for description of earthquake data and modeling of strain waves, faulting patterns, and subduction processes, including slow earthquakes and periodic episodic tremor and slow slip (ETS) effects.