  We define and study a generalization of the analytic Cauchy problem, that
specializes to the Cauchy-Kowaleskaya-Kashiwara problem in the linear case. The
main leitmotive of this text is to adapt Kashiwara's formulation of this
problem both to the relatively D-algebraic case and to the derived analytic
situation. Along the way, we define the characteristic variety of a derived
nonlinear partial differential system.
