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We study the effect of an optical lattice (OL) on the ground-state propertiesof one-dimensional ultracold bosons with three-body attraction and two-bodyrepulsion, which are described by a cubic-quintic Gross-Pitaevskii equationwith a periodic potential. Without the OL and with a vanishing two-bodyinteraction term, soliton solutions of the Townes type are possible only at acritical value of the three-body interaction strength, at which an infinitedegeneracy of the ground-state occurs; a repulsive two-body interaction makessuch localized solutions unstable. We show that the OL opens a stability windowaround the critical point when the strength of the periodic potential is abovea critical threshold. We also consider the effect of an external parabolictrap, studying how the stability of the solitons depends on matching betweenminima of the periodic potential and the minimum of the parabolic trap.

Ultracold Bosons with 3-Body Attractive Interactions in an Optical Lattice