Dmitrieva I. Analytical research methods of electromagnetic wave propagation in guided systems

Subject of inquiry - the processes of electromagnetic wave propagation in guided systems. Scope of research - constructive research methods of electromagnetic wave propagation with mathematical models as the systems of partial differential equations and the Landau-Lifshitz equation as the main analytic statement for the soliton study in ferromagnetic. The used research methods: linear operator theory and matrix theory; integral transform; ordinary differential equations; the inverse scattering problem; scalar Riemann problem; algebraic function theory. Theoretical and practical results: for the first time, two analytic methods of the electromagnetic field vector function construction are proposed basing on the diagonalization of the system of arbitrary operator equations with invertible and commutative in pairs elements over the finite-dimensional numerical space; for the first time, mathematical simulation of the electromagnetic wave propagation in the guided systems is done using the general statements of the boundary value problems whose explicit solutions are got by the improved integral transform method; for the first time, the exact method of the homogeneous matrix boundary value Riemann problem solution is proposed for the multi valued vector field function construction while coefficients of problem are non commutative permutation of not prime orders; for the first time, the uniform analytic solution of the Landau-Lifshitz equation in the general statements is suggested; new analytic research methods of the electromagnetic field wave propagation allow to construct correct mathematical models whose explicit solutions describe electrodynamic processes not using approximate numerical procedures; consideration of the heterogeneous media implies practical application for metamaterials; the explicit construction of the multi valued vector field function and its application to the exact solution of the Landau-Lifshitz equation allows investigating magnetic solitons in detail; the obtained results are valid for the mathematical simulation and design engineering of the microwave structures, and for the research in electronics and nanotechnology concerning creation of the nanomagnetic elements as well.