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This paper employs the extended rational sin–cos and sinh–cosh method to construct precise solutions to the nonlinear Schrödinger equation. It is illustrated that the proposed technique provides a foremost and effectual mathematical tool for solving numerous types of partial differential equations applied in mathematics, optics, physics, and chemical engineering. We obtain the consequences of periodic, dark, and bright solutions. Furthermore, we can imagine the acquired solutions by drawing two-dimensional and three-dimensional plots. [ABSTRACT FROM AUTHOR]