Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Par-tial Differential Equations (PDEs) with a particular application to the wave equation [15]. To do so, the author has introduced the notion of energy spaces included in the Schwartz space S ? (R). In this model, the key is to look at which ones of these subspaces are reduced to {0} with the help of energy opera-tors (and generalized energy operators). It leads to define additional solutions for a nominated PDE. Beyond that, this work intends to develop the concept of multiplicity of solutions for a linear PDE through the study of these energy spaces (i.e. emptiness). The main concept is that the PDE is viewed as a gen-erator of solutions rather than the classical way of solving the given equation with a known form of the solutions together with boundary conditions. The theory is applied to the wave equation with the special case of the evanescent waves. The work ends with a discussion on another concept, the duplication of solutions and some applications in a closed cavity.
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