The role of a continuous spectrum of linear perturbations of nonlinear solitary wave propagating at a constant velocity on the surface a thin liquid falling film on a vertical wall under the action of gravity has been studied. It is established that, at moderate Reynolds numbers, the dynamics of perturbations is determined by a function that possesses the properties of a discrete spectrum in the space of functions exhibiting exponential growth at minus infinity, rather than by the discrete spectrum or by estimates of the action of the continuous spectrum. This result indicates that the continuous spectrum has an integrable singularity whose decay coefficient is lower than a discrete eigenvalue.
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