Hidden properties of the equations of mathematical physics. Evolutionary relation for the state functionals and its connection with the field-theory equations

It is shown that the equations of mathematical physics describing material systems (material media) such as the thermodynamic, gas-dynamic and cosmic systems as well as the systems of charged particles and others have double solutions, and this fact enables one to describe the processes of emergence of various structures and formations (waves, vortices and so on). This follows from the evolutionary relation in skew-symmetric differential forms for state functionals (such as the action functional, entropy, Pointing's vector, Einstein's tensor, wave function, and others). This relation arises when studying the integrability of the equations of mathematical physics. The evolutionary relation has the properties of the field-theory equations. This fact discloses a connection of the field-theory equations with the equations of mathematical physics and enables one to understand the basic principles of the field theory and the properties of physical fields