Abstract
Abstract We consider biquaternionic wave (biwave) equations. They are biquaternionic generalizations of the Maxwell and Dirac equations and are equivalent to a system of eight differential equations of hyperbolic type. Using the theory of generalized functions, we construct fundamental and generalized solutions of such equations, including discontinuous ones, describing shock waves and obtain conditions on the fronts. A solution of the Cauchy problem for a biwave equation is constructed, and so are analogs of Kirchhoff–Green’s formulas that permit one to determine the solution inside a bounded domain given the boundary and initial values of the solution in this domain.