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The main objective of this paper is to investigate analytic soliton solutions of a nonlinear Schrödinger equation (NLSE), including Kudryashov’s sextic power-law nonlinearity by introducing different approaches of two efficient analytical methods. The considered equation has been recently introduced by N. A. Kudryashov to describe pulse propagation in optical fibers. The refractive index in the equation comprises six terms, each of the terms containing a power-law component.

Applying a wave transformation to the considered NLSE and splitting up the real and imaginary parts, the NLSE is converted to the nonlinear ordinary differential equations (NLODEs). Then, the solutions of NLODEs are considered as suggested in the proposed method and suggested solutions that include some unknown parameters are substituted into the NLODE. An algebraic equations system is acquired by collecting the …