Nonlinear Integro-Differential Models for Intense Waves in Media Like Biological Tissues and Geostructures with Complex Internal Relaxation-Type Dynamics

摘要

The paper discusses a universal scheme for constructing nonlinear integro-differential models to describe intense waves in media with a complex internal relaxation-type dynamics. Examples of such media are presented. Various forms of kernels are described. Situations are shown in which the models can be sim- plified by reducing them to differential or differential–difference equations with partial derivatives. Integral relations for the linear momentum and energy transferred by the wave are obtained. Exact solutions are found. The mapping method is used to obtain approximate solutions and analyze them in the form of differ- ence relations.