Abstract
The problem of the propagation of coupled surface electromagnetic waves in a two-layer cylindrical circular waveguide filled with an inhomogeneous nonlinear medium is considered. A nonlinear coupled TE-TM wave is characterized by two (independent) frequencies ωe and ωm and two propagation constants $${\widehat \gamma _e}$$ and $${\widehat \gamma _m}$$ . The physical problem reduces to a nonlinear two-parameter eigenvalue problem for a system of nonlinear ordinary differential equations. The existence of eigenvalues ( $${\widehat \gamma _e}$$ , $${\widehat \gamma _m}$$ ) in proven and intervals of their localization are determined.
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