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This study reveals the dark, bright, combined dark–bright, singular optical solitons and other solutions to the conformable space–time fractional Fokas–Lenells equation. We use two integral schemes in reaching such solutions. The constraints conditions which guarantee the existence of valid solutions are stated. By choosing the suitable values of the parameters involved, we plot the 2-dimensional and 3-dimensional surfaces to some of the obtained solutions. [ABSTRACT FROM AUTHOR]

In this paper, we investigate and use the new modified exp ( − Ω ( ξ ) ) -expansion method, (MEM). We apply the new MEM to nonlinear long–short-wave interaction systems (NLSWIS). Among our findings are sets of solutions including, but not limited to, new hyperbolic, complex, and dark soliton solutions. Not only is MEM shown to be highly adaptable for partial differential equations with strong nonlinearities, but also, it turns out to be highly efficient, despite its ease. [ABSTRACT FROM AUTHOR]

In this paper, we seek for the new soliton solutions to the coupled nonlinear Maccari's system by using sine-Gordon expansion method. Sine-Gordon expansion method is based on sine-Gordon Eq. (2.1) and a travelling wave transformation. We obtain new complex hyperbolic functions solutions to this system with help of Wolfram Mathematica 9, we also plot 3-dimensional and 2-dimensional graphics to some obtained solution using the same program in Wolfram Mathematica 9. Finally, we submit a comprehensive conclusions. [ABSTRACT FROM AUTHOR]

This study is related to new soliton solutions compound KdV-Burgers equation, generalized KdV equation and (2+1) dimensional Broer–Kaup equations with variable coefficients. The generalized Kudryashov method (GKM) has been tackled for procuring exact solutions of these equations. By using this method, dark and bright soliton solutions of these equations have been found. Also, some graphical representations have been given to observe the structure of these solutions. [ABSTRACT FROM AUTHOR]

In this paper, we consider exact solutions of Maccari system. We tackle extended trial equation method and generalized Kudryashov method to find exact solutions of this system. Initially, we obtain some exact solutions such as rational function solution, travelling wave solution, soliton solution, Jacobi elliptic function solution, hyperbolic function solution and periodic wave solution of this system by using extended trial equation method. Also, we attain dark soliton solutions of this system by using generalized Kudryashov method. Finally, for suitable parameter values, we plot two and three dimensional graphics of imaginary and real values of some exact solutions that we found by using both methods. [ABSTRACT FROM AUTHOR]