  Considering one of the fundamental notions of Bers' theory of pseudoanalytic
functions the generating pair via an intertwining relation we introduce its
generalization for biquaternionic equations corresponding to different
first-order systems of mathematical physics with variable coefficients. We show
that the knowledge of a generating set of solutions of a system allows one to
obtain its different form analogous to the complex equation describing
pseudoanalytic functions of the second kind and opens the way for new results
and applications of pseudoanalytic function theory. As one of the examples the
Maxwell system for an inhomogeneous medium is considered, and as one of the
consequences of the introduced approach we find a relation between the
time-dependent one-dimensional Maxwell system and hyperbolic pseudoanalytic
functions and obtain an infinite system of solutions of the Maxwell system.
Other considered examples are the system describing force-free magnetic fields
and the Dirac system from relativistic quantum mechanics.
