Department of Applied Mathematics,

Dalian University of Technology,

Dalian 116023,

P.R. CHINA

E-mail: meiqin-303@sohu.com

**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.