Use of geometric properties of three invariants in wave problems of hydrodynamics and electrodynamics

The theory of deformations is common to the theory of elasticity, hydrodynamics and electrodynamics. The conservation law for the deformation of the control figure contains linear, quadratic and cubic invariants. Passing to the limit of the derivation of the continuity equation destroys the quadratic and cubic invariants in the formula for the volume expansion coefficient. This simplification can lead to the loss of some fluid motion modes. This simplification can lead to the loss of some modes of behavior of electromagnetic fields. A method for taking into account three invariants in the solutions of the equations of hydrodynamics and electrodynamics is presented. For this, wave differential equations of the second and third order in time are used.