Hidden unique possibilities of mathematical physics equations (Formalism of skew-symmetric forms)

Abstract

It is shown that mathematical physics differential equations have properties that allow describing processes such as the structures emergence, discrete transitions, quantum jumps. The peculiarity is that such properties are hidden. They do not follow directly from the mathematical physics equations but are realized discretely in the solving process. This is due to the mathematical physics equations integrability, which, as shown, can be realized only discretely in the presence of any degrees of freedom. In this case, a transition occurs from the original coordinate space with a solution that is not a function (the solution derivatives do not compose a differential) to integrable structures with a solution that is a discrete function. It is the double solutions and spatial transitions that can describe the processes of the emergence of any structures or phenomena. Due to hidden properties, the mathematical physics equations have unique possibilities in describing physical processes and phenomena that cannot be described in the framework of other mathematical formalisms. Such results were obtained using skew-symmetric differential forms.