Abstract
The paper studies soliton solutions in couplers with optical metamaterials that are governed by the lately proposed Kudryashov's generalized form of power-law of refractive index. The low-count chromatic dispersion is also replenished with cubic-quartic dispersive effects. The couplers are of both kinds, namely twin-core couplers as well as multiple-core type. The auxiliary equation approach recovers a full spectrum of solitons that are exhibited with their necessary parameter restrictions.