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The main goal of the article is to present the optical soliton solutions of the nonlinear Schrodinger equation, comprising Kudryashov's quintuple power-law with dual form nonlinearity which has very important applications in domination soliton pulse propagation through optical fibers and photonic crystal fibers. To achieve our goal, two potent analytical techniques are employed: the Sardar-Subequation method and the new method G ′ k G ′ + G + r -expansion method, which represent a novel approach not found in existing literature. Furthermore, our approach offers distinctive solutions characterized by a rich variety of trigonometric and hyperbolic functions. The majority of our results are depicted graphically to highlight our achievements. [ABSTRACT FROM AUTHOR]

The nonlinear Schrödinger equation's natural protraction, the (2+1) Fokas system, illustrates how a pulse moves across monomode optical fibers. Three efficient methods the Sardar sub-equation approach, the Bernoulli sub-ODE method, and the generic Kudryashov's method are used in this study to offer various families of solutions. Several sorts of function solutions, including those for hyperbolic, trigonometric, power, exponential, and rational functions, are provided by our suggested approaches. In order to highlight the many solutions found, numerous graphs are given toward the conclusion of the text. [ABSTRACT FROM AUTHOR]