An algebraic analysis approach to certain classes of nonlinear partial differential systems

Many partial differential systems appearing in mathematical physics, engineering sciences and mathematical biology are nonlinear. Unfortunately, the algebraic analysis approach, based on module theory, can only handle linear partial differential systems. This paper is a first step toward a generalization of this approach to certain classes of nonlinear partial differential systems. In particular, we show how constructive methods of differential algebra and algebraic analysis can be used to extend recent results on internal symmetries, conservation laws and the decomposition problem to these classes of nonlinear partial differential systems.