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Propagation of electromagnetic waves in a shielded dielectric layer with cubic nonlinearity

An eigenvalue problem describing propagation of transverse magnetic waves in a shielded dielectric layer with cubic nonlinearity is studied. It is proved that even for small value of the nonlinearity coefficient, the nonlinear problem has infinitely many nonperturbative solutions (eigenvalues and eigenfunctions), whereas the corresponding linear problem always has a finite number of solutions.