Modeling Nonlinear Partial Differential Equations in an Inductive Electrical Line and Construction of Implicit Wave Solutions

In this work, we model the nonlinear partial differential equations that describe the dynamics of propagation of signals (waves) in the carefully constructed inductive power line. This modeling is based on the appropriate choice of the magnetic flux of connection between the inductors in the electric line. The signals sought are naturally the solutions of the partial differential equations obtained for this purpose. These equations not being easily integrable, it is advisable for us to make the choice of the forms of solutions to be constructed. Faced with the need to make the right choice, we use the iB-function with unknown characteristics as a basic signal to finally determine with exactness the solution functions (signals) via the notion of probability of appearance of the characteristic indices of the iB-function in the general equation of range.