We consider the characteristics of magnetohydrodynamic wave modes in a model of a nonuniform and asymmetric coronal magnetic slab with continuous boundaries. We take into account both the asymmetry of the internal structure of the slab and the asymmetric external environment. For the biexponential asymmetric transverse profile of the background plasma density, we obtain the governing dispersion relation, which is then analyzed both numerically and analytically. The principal kink and sausage modes are found to have mixed properties in the asymmetric slab. Both internal and external asymmetries in the slab structure have no prominent effect on the dispersion properties of fast waves, except for the principal kink mode, which can be in the trapped or leaky regime in an asymmetric exterior. However, the effect of asymmetries is significant on the spatial transverse structure of the principal fast modes. In the asymmetric background, the kink mode results in both the transverse displacement of the slab and the distortion of its cross section. In turn, the principal sausage mode in an asymmetric magnetic slab causes the expansion and contraction of the slab, as well as its oscillatory transverse motion. Moreover, in this context, the effect of internal asymmetry is much stronger than the effect of an asymmetric external medium. These mixed properties suggest that the principal kink and sausage modes can be detected in both intensity and Doppler shift fluctuations. The application of the results to the interpretation of the observed oscillations in coronal magnetic structures is discussed.
I. Lopin (Sun,) studied this question.