General solutions’ laws of linear partial differential equations I

Abstract

Z2and Z3transformations are proposed for the first time in this paper, combined with the previously proposed Z1transformation, the general solutions of many kinds of n-ary m-order linear partial differential equations (PDEs), including the famous transport equation are obtained for the first time. Some first-order linear PDEs that cannot be solved by the characteristic equation method can be solved by Z transformations. Using the general solutions, we also obtain the exact solutions of some definite solution problems.

Keywords

• Z1transformation
• Z2transformation
• Z3transformation
• General solutions
• The transport equation
• Schrödinger equation