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Martynova, Valeria; Valovik, Dmitry
Journal of Differential Equations, 09/2023, Letnik: 367Journal Article
We consider a problem of propagation of monochromatic electromagnetic waves in a circle cylindrical waveguide filled with nonlinear dielectric medium. The permittivity of the waveguide is described by the Kerr law, which is one of the most important nonlinear dependence in nonlinear optics. In order to find guided waves we develop an original mathematical approach that allows us to prove existence of infinitely many guided waves. In addition, we prove that only a finite number of the founded nonlinear guided waves have linear counterparts; the others are nonlinearizable solutions. Numerical results are also presented.
