Abstract
<abstract><p>The soliton solutions are one of the stable solutions where nonlinearity and dispersion are perfectly balanced. They are used in a wide variety of physical fields, including plasma, solid state, neuronal, biological production, and diffusion processes. Different analytical methods have been used until now to obtain the soliton solutions of the Sawada-Kotera (SK) equation. The purpose of this study is to offer two successful analytical methods for solving the classical (1+1) dimensional Sawada-Kotera (SK) equation. In order to solve the partial differential equation (PDE), both the modified auxiliary equation method (MAEM) and the extended direct algebraic method are applied. The classical fifth-order SK equation is examined in this study, leading to a variety of precise soliton solutions, including single, periodic, and dark soliton, which are obtained analytically. To illustrate the effect of the parameters, the results are shown in graphical form.</p></abstract>
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