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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]

This work addresses the analytical investigation of the prey–predator behavior modeled by nonlinear evolution equation systems with fractional derivative order. Through the New Extended Algebraic Method (NEAM), we unearthed diverse types of soliton solutions including bright, dark solitons, combined trigonometric function solutions, and singular solutions. Besides the results obtained in the work of Khater, some new complex soliton solutions are also unearthed. The NEAM can also be used like the synthesis of the two mathematical tools. [ABSTRACT FROM AUTHOR]