Theory of Nonlinear Ferromagnetic Resonance in the Samples with Magnetostatic and Exchange Boundary Conditions Imposed

General theory of nonlinear ferromagnetic resonance is presented for samples with the usual magnetostatic and exchange boundary conditions imposed at the sample surface. In such samples the Suhl instabilities and other nonlinear effects occur due to nonlinear interactions of magnetostatic or dipole-exchange modes. All relevant types of interactions are included in the Hamiltonian: with the pumping field, three- and four-mode ones. Analytic calculation of the Suhl thresholds in the three possible types of instabilities in perpendicular and parallel pumping is performed for the sample in the shape of a thin slab.