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In this study, a new method called improved Bernoulli sub-equation function method has been proposed. This method is based on the Bernoulli sub-ODE method. After we mention the general properties of proposed method, we apply this algorithm to the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation system. This gives us some new prototype solutions such as exponential and rational function solutions. Then, we have plotted two- and three-dimensional surfaces of analytical solutions. Finally, we have submitted a comprehensive conclusion. [ABSTRACT FROM AUTHOR]

In this study, we obtain some new complex analytical solutions to the Kundu–Eckhaus equation which seems in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics using improved Bernoulli sub-equation function method. After we have mentioned the general structure of improved Bernoulli sub-equation function method, we have successfully applied this method and then obtained some new complex hyperbolic and complex trigonometric function solutions. Two- and three-dimensional surfaces of analytical solutions have been plotted via wolfram Mathematica 9 version. At the end of this article, a conclusion has been submitted by mentioning important points founded in this study. [ABSTRACT FROM AUTHOR]

In this manuscript, we consider the Bernoulli sub-equation function method for obtaining new exponential prototype structures to the Cahn–Allen mathematical model. We obtained new results using this technique. We plotted two- and three-dimensional surfaces of the results using Wolfram Mathematica 9. At the end of this manuscript, we submitted a conclusion in a comprehensive manner. [ABSTRACT FROM AUTHOR]