We analyse the dispersion relation of ripplons, on the surface of superfluid helium, using the dispersive hydrodynamics approach and find a new ripplon branch. We obtain an analytical equation for the dispersion relation and analytic expressions for the limiting cases. The probabilities of decay of unstable ripplons above the roton gap into rotons are derived. A numerical solution for the ripplon dispersion curve is obtained. A new ripplon branch is found at energies just below the instability point of the bulk spectrum, and is investigated; its stability is discussed.
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