Аннотация:show that the equations of mathematical physics that describe real processes and include the equa-tions of the conservation laws for energy, momentum, moment of momentum, and mass have a peculiarfeature. The conservation law equations turn out to be inconsistent. This produces the integrability of themathematical physics equations and the specific features of their solutions, namely the presence of doublesolutions: on a nonintegrable coordinate space and on integrable structures. As a consequence, we candescribe evolutionary processes, such as the emergence of discrete structures and observable formations(waves, vortices, turbulent pulsations).