Abstract
This context focuses on examining the manner in which localized waves travel through a non-linear medium that adheres to a dual-power law. This medium encompasses a range of disruptions like inter modal dispersion, self frequency shift, and self-steepening effects. This investigation entails employing an improved modified extended tanh function (IMETF) technique to obtain various novel optical soliton solutions which include bright, dark, singular and combo singular-dark solitons. Furthermore, we extract singular periodic, exponential, rational, and Weierstrass elliptic solutions. To showcase their physical characteristics, we provide graphical representations in 3D and 2D of some of the derived solutions.
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