Abstract
Surface excitations of a nonideal Bose gas are investigated within the Gross-Pitaevskii equation linearized near the kink solution. The resulting matrix Schrödinger equation with supersymmetric potentials describes two Goldstone (gapless) modes which are localized by these potentials near the free surface. The first mode represents an ordinary capillary wave (ripplon) and the second one corresponds to a surface weakly trapped phonon. The last one might additionally contribute to the surface tension of helium II explaining the discrepancy between experiment and theory.
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