The class of second order quasilinear equations: models, solutions and background of classification

The paper is concerned with the unsteady solutions to the model of mutually penetrating continua and quasilinear hyperbolic modification of the Burgers equation (QHMB). The studies were focused on the peculiar solutions of models in question. On the base of these models and their solutions, the ideas of second order quasilinear models classification were developed.