[INVITED] Soliton propagation through nanoscale waveguides in optical metamaterials

•Soliton solutions in optical metamaterials are obtained.•Bright, dark and singular soliton solutions are recovered.•Five types of nonlinear media are studied.

This paper studies the dynamics of soliton propagation through optical metamaterials. The proposed model will be studied with five forms of nonlinearity. They are Kerr law, power law, parabolic law, dual-power law and log-law. The integration scheme that will be adopted is the method of undetermined coefficients. Bright, dark and singular soliton solutions will be obtained. The essential conditions for the existence of these solitons will naturally emerge.