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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 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]