Decomposition of Solutions of the Cauchy Problem of a Quasi-Homogeneous Partial Differential Equation

Abstract

We give a decomposition formula for the formal solution of the Cauchy problem for a quasi-homogeneous partial differential equation with constant coefficients in the two-dimensional complex plane. The decomposition formula, Theorem 1.1, is given in a form associated with the factorization of the relevant operator which is similar to the decomposition of the solution of an ordinary differential equation with constant coefficients.