Abstract
The main goal of this article is to investigate the optical soliton solutions for the cubic–quartic (CQ) twin-core couplers and multiple-core couplers having optical metamaterials with parabolic non-local law nonlinearity and nonlinear perturbation terms. The couplings with nearest neighbors and with all neighbors are discussed. The unified Riccati equation expansion approach and the addendum to Kudryashov’s approach are applied. Straddled, combo-bright-singular, dark, bright, singular solitons solutions as long as periodic and rational solutions are found.