On the Existence of Nonlinearizable Solutions of a Nonclassical Two-Parameter Nonlinear Boundary Value Problem

A nonlinear eigenvalue problem for a system of three equations with boundary conditionsof the first kind, describing the propagation of electromagnetic waves in a plane nonlinearwaveguide, is considered. This is a two-parameter problem with one spectral parameter and asecond parameter arising from an additional condition. This condition connects the integrationconstants that arise when finding the first integrals of the system. The existence of nonlinearizablesolutions of the problem is proved.