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  • 1.
    Shestopalov, Yury
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electronics, Mathematics and Natural Sciences, Mathematics.
    Complex waves in a dielectric waveguide2018In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 82, p. 16-19Article in journal (Refereed)
    Abstract [en]

    Existence of two families of symmetric complex waves in a dielectric waveguide of circular cross section is proved. Eigenvalues of the associated Sturm–Liouville problem on the half-line are determined. 

  • 2.
    Shestopalov, Yury
    et al.
    University of Gävle, Faculty of Engineering and Sustainable Development, Department of Electrical Engineering, Mathematics and Science, Mathematics.
    Smolkin, Eugene
    Smirnov, Yury
    Department of Mathematics and Supercomputing, Penza State University, Krasnaya Str. 40, Penza, 440026, Russia.
    On the existence of the nonlinear leaky TE-polarized waves in a metal–dielectric cylindrical waveguide2019In: Wave motion, ISSN 0165-2125, E-ISSN 1878-433X, Vol. 91, article id 102378Article in journal (Refereed)
    Abstract [en]

    We consider propagation of leaky waves in the Goubau line (a perfectly conducting cylinder covered by a concentric dielectric layer) filled with nonlinear inhomogeneous medium. The problem is reduced to the analysis of a nonlinear integral equation with a kernel in the form of the Green’s function of an auxiliary boundary value problem on an interval. The existence of propagating nonlinear leaky waves for the chosen nonlinearity (Kerr law) is proved using the method of contraction. Conditions under which a finite number of waves can propagate are obtained and the intervals of localization of the corresponding propagation constants are determined. For the numerical solution, a method based on solving an auxiliary Cauchy problem (a version of the shooting method) is proposed. In numerical experiments, two types of nonlinearities are considered and compared: Kerr nonlinearity and nonlinearity with saturation. New propagation regimes are discovered.

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