On a Novel Approach to Decompose Finite Energy Functions by Energy Operators and its Application to the General Wave Equation

This work aims at introducing some energy operators linked to the Teager-Kaiser energy operator and expands it from time to space in the real domain. We then show the decomposition of the functions of space and time differentiable at least twice in R using those energy operators. The second part of the work focuses on using the energy operators to redefine the general wave equation. The method is first established for the wave equation in a non-dispersive medium and then extended for a particular case of the wave equation in a dispersive medium. Through the method, the author defines the energy quantities Σ− and Σ+ associated for a given solution of the wave equation (f). An important property (Property 3) shows that there are unique energy quantities (Σ−, Σ+) associated with the absolute value of a given solution of the wave equation. Some examples are used to look into the theory. Mathematics Subject Classification: 35-02