Open AccessInvestigation of the existence domain for Dyakonov surface waves in the Sage computer algebra system
Author(s) -
Oleg K. Kroytor
Publication year - 2021
Publication title -
discrete and continuous models and applied computational science
Language(s) - English
Resource type - Journals
eISSN - 2658-7149
pISSN - 2658-4670
DOI - 10.22363/2658-4670-2021-29-2-114-125
Subject(s) - symbolic computation , isotropy , surface (topology) , tensor (intrinsic definition) , dielectric , plane (geometry) , algebraic number , physics , plane wave , interface (matter) , domain (mathematical analysis) , algebraic equation , anisotropy , mathematical analysis , mathematics , algebra over a field , pure mathematics , geometry , quantum mechanics , nonlinear system , gibbs isotherm , surface tension
Surface electromagnetic waves (Dyakonov waves) propagating along a plane interface between an isotropic substance with a constant dielectric constant and an anisotropic crystal, whose dielectric tensor has a symmetry axis directed along the interface, are considered. It is well known that the question of the existence of such surface waves is reduced to the question of the existence of a solution to a certain system of algebraic equations and inequalities. In the present work, this system is investigated in the Sage computer algebra system. The built-in technique of exceptional ideals in Sage made it possible to describe the solution of a system of algebraic equations parametrically using a single parameter, with all the original quantities expressed in terms of this parameter using radicals. The remaining inequalities were only partially investigated analytically. For a complete study of the solvability of the system of equations and inequalities, a symbolic-numerical algorithm is proposed and implemented in Sage, and the results of computer experiments are presented. Based on these results, conclusions were drawn that require further theoretical substantiation.