In this paper, we have established the new exact solitons solutions of the nonlinear Biswas–Arshed equation which are used to study soliton dynamics in optical fibers, pivotal cloud foundry (PCF) and metamaterials via the prominent approach, known as auxiliary equation method. The obtained solutions disclosed that the suggested method is the essential addition for studying the exact solution of nonlinear Biswas–Arshed equation.

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