Abstract
The Lin-Shu dispersion relation is applicable in the (asymptotic) case of tight spirals (large wave numberkR). Here we reconsider the various steps leading to the Lin-Shu dispersion relation in higher approximation, under the assumption that the wave numberkR is not large [(kRr) =O(1)], and derive a new dispersion relation. This is valid for open spiral waves and bars. We prove that this dispersion relation is the appropriate limit of the nonlinear self-consistency condition in the case where the linear theory is applicable.
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