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Numerical Technique for Determining the Bifurcation Points of the Nonlinear Maxwell Operator (Maxwell’s Equations Together with the Landau–Lifshitz Equation)

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Abstract

A computational algorithm is constructed, which implements a numerical analysis of the bifurcation points of the nonlinear Maxwell operator (the system of Maxwell equations together with the Landau–Lifshitz equation). Numerical analysis of branch points of nonlinear Maxwell equations is carried out under the assumption that one solution in the vicinity of a singular point is known and obtained using a decomposition computational algorithm, which is then “enhanced” by a qualitative method of branch point analysis. Necessary and sufficient conditions for the existence of bifurcation points for the eigenvalues of the linearized Maxwell operator are formulated.

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REFERENCES

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ACKNOWLEDGMENTS

In the part concerning the development of the computational method and the algorithm implementing it, O.A. Golovanov was a coauthor.

Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

  1. Instrumentation, Information Technology and Electronics Faculty, Penza State University, 440026, Penza, Russia

    G. S. Makeeva

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  1. G. S. Makeeva
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Correspondence to G. S. Makeeva.

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The author declares that she has no conflicts of interest.

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Translated by N. Wadhwa

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Makeeva, G.S. Numerical Technique for Determining the Bifurcation Points of the Nonlinear Maxwell Operator (Maxwell’s Equations Together with the Landau–Lifshitz Equation). Tech. Phys. 68, 180–182 (2023). https://doi.org/10.1134/S1063784223070010

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  • DOI: https://doi.org/10.1134/S1063784223070010

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