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The double-gradient model of flapping oscillations is generalized for oblique plane waves, propagating in the equatorial plane. It is found that longitudinal propagation ( = 0) is prohibited, while transversal ( = 0) or nearly transversal waves should possess a maximum frequency, diminishing with the reduction of ratio. It turns out that the sausage mode may propagate in a narrow range of directions only, . A simple analytical expression for the dispersion relation of the kink mode, valid in most part of wave numbers range, , is derived.


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