Dirichlet series and the integrability of multilinear differential equations

We explore the relationship between the integrability of nonsemilinear partial differential equations and formal Dirichlet series solutions. To this end we consider a variety of integrable and nonintegrable differential equations. We also demonstrate that such series solutions are a natural extension to the nonlinear case of those obtained by basic solution techniques for linear ordinary differential equations. (C) 2005 American Institute of Physics.