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In this work, the generalized Kudryashov method is used to obtain the exact traveling wave solutions for two important nonlinear evolution equations, the Chaffee–Infante equation in (2 + 1)‐dimensions and the dimensionless Zakharov equation. The generalized Kudryashov method is successfully used for getting exact solutions of these nonlinear equations in the form of exponential function solutions and hyperbolic function solutions. Moreover, we have discussed the dynamical behaviors through graphical representation of the solutions obtained in this way. [ABSTRACT FROM AUTHOR]

In this paper, we combine the unified and the explicit exponential finite difference methods to obtain both analytical and numerical solutions for the Newell‐Whitehead‐Segel–type equations which are very important in mathematical biology. The unified method is utilized to obtain various solitary wave solutions for these equations. Numerical solutions of the specific case studies are investigated by using the explicit exponential finite difference method ensures the accuracy and reliability of the proposed scheme. After obtaining the approximate solutions, convergence analysis and error estimation (the error norms and absolute errors) are presented by comparing these results with the analytical obtained solutions and other methods in the literature through tables and graphs. The obtained analytical and numerical results are in good agreement. [ABSTRACT FROM AUTHOR]

In this paper, we consider conservation laws and exact solutions of the (3+1)-dimensional modified KdV–Zakharov–Kuznetsov equation. Firstly, we construct conservation laws of the given equation with the help of the conservation theorem; the developed conservation laws are modified conservation laws. Then, we obtain exact solutions of the given equation via the ( G ′ / G , 1 / G )-expansion method. The obtained solutions are classified as trigonometric solutions, hyperbolic solutions and rational solutions. Furthermore, graphical representations of the obtained solutions are given. [ABSTRACT FROM AUTHOR]