Linearization of Cauchy's Problem for Quadratic Semilinear Partial Differential Equations

The technique of linearization is applied to quadratic semilinear systems of n first-order partial differential equations. By introducing a related linear algebra A, we combine analytic and algebraic arguments to obtain a class of linearizable systems. We relate the coefficients of such systems to the center of A and show that, for hyperbolic systems, the ideals of A decouple the system into disjoint subsystems each having its own single wave number.