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In this paper, using the extended rational sine–cosine and rational sinh–cosh methods, we find new soliton solutions for the Klein–Gordon–Zakharov equations. The extended rational sine–cosine and rational sinh–cosh methods are prospering in finding soliton solutions of the Klein–Gordon–Zakharov equations. By means of these methods, we found some young solitons of the above mentioned equation. The conclusions we receive are dark, bright, and periodic. In addition, in order to imagine the underlying dynamics of the obtained soliton solutions, 2D and 3D plots are drawn. [ABSTRACT FROM AUTHOR]

In the current paper, we carry out an investigation into the exact solutions of the (3+1)-dimensional space-time fractional modified KdV--Zakharov--Kuznetsov (fractional mKdV--ZK) equation. Based on the conformable fractional derivative and its properties, the fractional mKdV--ZK equation is reduced into an ordinary differential equation which has been solved analytically by the variable separated ODE method. Various types of analytic solutions in terms of hyperbolic functions, trigonometric functions and Jacobi elliptic functions are derived. All conditions for the validity of all obtained solutions are given. [ABSTRACT FROM AUTHOR]