We construct wormholes in Einstein-scalar-Gauss-Bonnet theories with a potential for the scalar field that includes a mass term and self-interaction terms. By varying the Gauss-Bonnet coupling constant we delimit the domain of existence of wormholes in these theories. The presence of the self-interaction enlarges the domain of existence significantly. There arise wormholes with a single throat and wormholes with an equator and a double throat. We determine the physical properties of these wormholes including their mass, their size and their geometry.
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