Description of a class of evolutionary equations in ferrodynamics

In this paper, we state the problem of constructing evolution equations describing the dynamics of condensed matter with an internal structure. Within the framework of this statement, we describe the class of evolution equations for vector and pseudovector fields on $\mathbb{R}^3$ with an infinitesimal shift defined by a second-order, divergent-type differential operator, which is invariant under translations of $\mathbb{R}^3$ and time translations and is transformed covariantly under rotations of $\mathbb{R}^3$. The case of equations of this class with preserved solenoidality and unimodality of the field is studied separately. A general formula for all operators corresponding to these equations is established.