  Interaction of spiral density waves with stars in the vicinity of the inner
Lindblad resonance in galactic discs is investigated using the linear
perturbation theory and the leading orders in the epicyclic and WKB
approximations. In analogy with shear flows in hydrodynamics, we conjecture
that a weak nonlinearity in a narrow resonance region modifies the standard
(Landau-Lin) bypass rule of the singularity to the integration in the principal
value sense. This indeed leads to the reflection of the spiral wave instead of
absorption, but the detailed picture looks awkward: the intervals of the wave
weakening alternate with the intervals of the wave growth, so that the net
absorption is absent. Incidentally, we rectify the result concerning leading
spiral waves obtained earlier for the standard bypass rule.
