Abstract
We use the generalised nonlinear Schrödinger equation in this research work to study the localised wave propagation in a dual-power law medium that shows perturbations’ effects such as in inter-modal dispersion, shift in the self-frequency, and self-steepening. The modified extended mapping method (MEMM) is used to perform the study. Exact solutions and additional types of solitons are obtained. These solutions include Weierstrass elliptic solutions, singular periodic solutions, and {bright, dark, and singular} solitons. The retrieved solutions show how robust and efficient the current approach is. The physical attributes of the established solutions are illustrated by the visual representation of several selected solutions.
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