In this article, two different fifth-order nonlinear evolution equations (NLEEs), namely the (2+1)-dimensional bidirectional Sawada-Kotera (bSK) and the (2+1)-dimensional variable-coefficient Sawada-Kotera (SK) equations are investigated, whose generous exact solutions are formally generated, respectively. The paper proceeds step-by-step with increasing detail about derivation processes, first illustrating the algorithms of the proposed approach and then exploiting an even deeper connection between the derived solitary solutions with the assumed solution form. After applying a special trial function along with the related Hirota bilinear equations to handle these two cases a variety of traveling wave solutions are extracted, naturally including solitary wave and periodic wave ones. Moreover, via specifying values to the free parameters the physical explanations of the extracted solutions are depicted in detail. Particularly, the results indicate that free parameters can drastically influence the existence of solitary waves, their nature, profile, and stability. They are applicable to enrich the dynamical behavior of the associated nonlinear wave models. Finally, it is shown that the presented methodized resolution is straightforward and applicable to solve other NLEEs.

本文介绍了两个不同的五阶非线性演化方程（NLEE），即（2 + 1）维双向Sawada-Kotera（bSK）和（2 + 1）维变系数Sawada-Kotera（SK）研究了方程，分别正式生成了它们的大量精确解。本文逐步介绍了有关推导过程的更多细节，首先说明了所提出方法的算法，然后利用推导的孤立解与假定的解形式之间更深的联系。在应用特殊的试验函数以及相关的Hirota双线性方程式来处理这两种情况后，提取了各种行波解，自然包括孤波和周期波。此外，通过为自由参数指定值，详细描述了提取溶液的物理解释。尤其是，结果表明，自由参数可以极大地影响孤立波的存在，其性质，轮廓和稳定性。它们适用于丰富相关非线性波模型的动力学行为。最后，表明所提出的方法化解决方案是直接的，并且适用于解决其他NLEE。