On the methodology of variational representation of generalized solutions to quasi-linear hyperbolic two-equations systems

The paper contains further detailing of earlier formulated new approach to the study of quasi-linear hyperbolic systems on the basis of variational approach. The elaboration is got for the systems of two equations. It is shown that each characteristic field can be represented as the solution of certain variation calculus problem. At this the Hugoniot relations at the characteristics’ bents or when the characteristics of the same family intersect are fulfilled automatically. Also the paper describes the experience of numerical scheme construction on the basis of variational approach in the simplest case of Hopf equation. The work is written with “physical” level of rigor.