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In this article, we investigate the optical soiltons and other solutions to Kudryashov's equation (KE) that describe the propagation of pulses in optical fibers with four non-linear terms. Non-linear Schrodinger equation with a non-linearity depending on an arbitrary power is the base of this equation. Different kinds of solutions like optical dark, bright, singular soliton solutions, hyperbolic, rational, trigonometric function, as well as Jacobi elliptic function (JEF) solutions are obtained. The strategy that is used to extract the dynamics of soliton is known as Φ 6 -model expansion method. Singular periodic wave solutions are recovered and the constraint conditions, which provide the guarantee to the soliton solutions are also reported. Moreover, modulation instability (MI) analysis of the governing equation is also discussed. By selecting the appropriate choices of the parameters, 3D, 2D, and contour graphs and gain spectrum for the MI analysis are sketched. The obtained outcomes show that the applied method is concise, direct, elementary, and can be imposed in more complex phenomena with the assistant of symbolic computations. [ABSTRACT FROM AUTHOR]

We successfully apply extended rational sine-cosine/sinh-cosh and advance expansion function techniques in this paper. Various kinds of soliton solutions to the conformable time-fractional resonant nonlinear Schrödinger equation (RNLSE) in optical fiber are extracted. We discuss the system with the effects of coefficients like group velocity dispersion, non-Kerr nonlinearity, resonant nonlinearity, and construct optical soliton solution in terms of rational, trigonometric and hyperbolic function solutions with arbitrary parameters. The recovered solutions reveal that the applied approaches are straightforward and efficient to work out the excellent contribution for analyzing several classes of nonlinear partial differential equations (NLPDEs) in engineering and sciences. Moreover, 3D, 2D and contour graphs are sketched with suitable selection of the parameters under the criteria of constraints conditions. [ABSTRACT FROM AUTHOR]