Optical solitons to the nonlinear Schrödinger equation in metamaterials and modulation instability

Throughout this paper, we investigate the propagation of solitary waves in metamaterials. Indeed, we focus our attention on a nonlinear evolution equation, namely the nonlinear Schrodinger equation (NLSE) that models the dynamic of waves in such materials. Investigating solitons structures of such an equation, we make use for the purpose, of a mathematical tool which is a new generalized extended direct algebraic method (NGEDAM). As a results, rich solution structures are constructed analytically to which new solutions are provided to complete the ones already obtained elsewhere. In addition, the modulation instability (MI) analysis has been studied by employing the linearizing technic. We highlight the effects of the self-steepening (SS) associated to metamaterials parameters on MI bands. The obtained results have set up the W-shaped profile of the optical soliton solutions, which will certainly improve the communication over the optical fibers in diverse modes.