On the existence of infinitely many nonperturbative solutions in a transmission eigenvalue problem for nonlinear Helmholtz equation with polynomial nonlinearity

•Phenomenon of nonlinear electromagnetic wave propagation is considered.•The problem is formulated with physically realistic conditions.•It is proved the existence of a novel (nonlinear) guided regime.•The existence of a nonperturbative effect is proved.•An original analytic approach is used to stud...

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