Abstract
Analytical study of electromagnetic wave propagation is done in the case of isotropic inhomogeneous lines in the presence of the so called expofunctional influences. Mathematical simulation is based on the corresponding boundary problems whose PDE (partial differential equation) is the general wave one regarding the unknown electromagnetic field intensities. This PDE, in its turn, is generated by the specific form of differential Maxwell system. Solvability criterion of the latter is proved in terms of equivalence to the general wave equation in the class of non generalized functions. Those boundary problems explicit solutions are suggested using classical integral transform method.Reference 20.
Highlights
Analytical study of electromagnetic wave Further, in the case of systems of ODEs that are responsible for the mogeneous lines in the presence of the so called simplest, even trivial, vector field modeling, an exexpofunctional influences
Mathematical simulation plicit solution is not of great problem. It concerns is based on the corresponding boundary problems diagonalization procedure reducing initial matrix whose PDE is the system to the equivalent union of scalar equations general wave one regarding the unknown with respect to only one component of unknown electromagnetic field intensities
Turning to the suggested inverse matrix operator method, it is easy to guess that complication of matrix structure and increase of its dimension sharply exaggerates determinant study and creation of solvability conditions
Summary
Mathematical simulation plicit solution is not of great problem It concerns is based on the corresponding boundary problems diagonalization procedure reducing initial matrix whose PDE (partial differential equation) is the system to the equivalent union of scalar equations general wave one regarding the unknown with respect to only one component of unknown electromagnetic field intensities. As far as it is turn, is generated by the specific form of differential known, most naturally applied statement of the Maxwell system Solvability criterion of the latter is finite-dimensional system of PDEs dealing with proved in terms of equivalence to the general wave general mathematical simulation of electromagnetic equation in the class of non generalized functions. The goal of the given paper is mathematical modeling of the specific electromagnetic wave propagation governed by (1) and analytical study of improved boundary problems from [3] for excited inhomogeneous case
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