On the dimension of the solution space of a system of PDEs

Abstract:
Finding of the standard form of a system of PDEs and determination of the dimension of its solution space is an important part in the Riquier-Janet theory. The dimension of the solution space is characterized by the number of parametric derivatives. In present contribution, we try to put forward a new definition of the dimension of solution space of a system of PDEs, which can be uniquely determined due to independence of order and be compatible with physical phenomena.