Using the Geometric Properties of Three Invariants in Wave Problems of Hydrodynamics and Electrodynamics

Deformation theory is common to the theories of elasticity, hydrodynamics, and electrodynamics. The law of conservation for the deformation of a control figure contains linear, quadratic, and cubic invariants. Moving to the limit of deriving the continuity equation destroys the quadratic and cubic invariants in the formula for the coefficient of volume expansion and the equation of continuity. This simplification can result in the loss of some modes of fluid motion and descriptions of the possible behavior of electromagnetic fields. A way of considering the three invariants in solutions to equations of the hydrodynamics and electrodynamics is presented in this work. It is proposed that second- and third-order wave differential equations of time be used to describe the motion of a fluid and the behavior of a magnetic field’s strength with allowance for quadratic and cubic invariants.