Nonlinear differential systems: A canonic, multivariable theory

An attached (multivariable) nonassociative algebra is shown to be a useful tool for the study of general polynomic differential systems. The main result is that the theory allows the reduction of all such systems to the canonic quadratic form x
^·
= x ċ x within the algebra. This canonic square law differential equation is obtained through multivariable introductions to make all terms quadratic; nonstationary systems are included as are nonpolynomic differential systems through approximation. In the algebra a canonical power series solution is found which is useful for computer aided analysis. Examples are given to illustrate the concepts.