Abstract

We report exact bright and dark solitary wave solution of the nonlinear Schrodinger equation (NLSE) in cubic–quintic non-Kerr medium adopting phase–amplitude ansatz method. We have found the solitary wave parameters along with the constraints under which bright or dark solitons may exist in such a media. Furthermore, we have also studied the modulation instability analysis both in anomalous and normal dispersion regime. The role of fourth order dispersion, cubic–quintic nonlinear parameter and self-steeping parameter on modulation instability gain has been investigated.

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