A study is made of the influence of nonlinearity upon the structure of a steadystate disturbance brought about by low-frequency (ω ω i ) monochromatic magnetosound propagating in a transversally inhomogeneous low-pressure plasma (β m e /m i ), in the vicinity of the Alfvén resonance point for the case when the principal linear mechanism for forming the transverse structure is provided by magnetic field diffusion due to small plasma resistivity. It is shown that the nonlinear properties of the fundamental harmonic of a disturbance are determined by its self-action through a plasma density variation that it produces. The disturbance structure in the region of the Alfvén resonance is described.

A description of the evolution of the initial disturbance in the fast magnetosonic (FMS) waveguide in transversely inhomogeneous plasma, given a weak coupling between FMS and Alfven modes, is made. It is shown that the Fourier transform of the FMS waveguide disturbance with respect to the coordinates along which plasma is homogeneous can be presented as a superposition of collective modes of the leading approximation with respect to the weak FMS–Alfven wave coupling from the initial instant of time. Frequencies of such collective modes and dependence of their structures on the coordinate along the inhomogeneity are found without taking the FMS–Alfven resonance into consideration, and the mode decrements are calculated using the perturbation technique. On the basis of such a representation of the FMS waveguide disturbance, the evolution of Alfven waves generating with waveguide mode packets produced by the initial disturbance of an arbitrary longitudinal structure is described. It is shown that the longitudinal structure of the Alfven disturbance generated by the collective mode packet is determined by the ratio between longitudinal scales of the initial disturbance and scales specified by resonance conditions (the resonance longitudinal wave number and the width of the range of the resonance longitudinal wave numbers). The structures of Alfven disturbances for the cases of such different ratios are described.

For a cold plasma that is inhomogeneous (in the direction across an external homogeneous magnetic field), the nonlinear equation describing the spatial structure and temporal behaviour of a non-stationary disturbance in a resonance layer is obtained. The matching conditions for a disturbance through the resonance layer are obtained, and in the linear limit give a well-known linear matching. It is shown that the spatial and temporal behaviour of the resonance disturbance and the evolution of the resonant absorption in terms of nonlinear theory are determined by the ratio of the nonlinear to linear non-stationary spatial scales. The spatial–temporal profile of the disturbance in the resonance layer and the resonant absorption for different values of this ratio are calculated. A nonlinear decrease in the resonant absorption and a stratification of the resonance disturbance are revealed.

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