The nonlocal symmetry of the Sawada–Kotera (SK) equation is constructed with the known Lax pair. By introducing suitable and simple auxiliary variables, the nonlocal symmetry is localized and the finite transformation and some new solutions are obtained further. On the other hand, the group invariant solutions of the SK equation are constructed with the classic Lie group method. In particular, by a Galileo transformation some analytical soliton-cnoidal interaction solutions of a asymptotically integrable equation are discussed in graphical ways.

中文翻译：

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Sawada-Kotera 方程的非局部对称性和相互作用解的定位

Sawada-Kotera (SK) 方程的非局部对称性是用已知的 Lax 对构造的。通过引入合适且简单的辅助变量，对非局部对称性进行局部化，进一步得到有限变换和一些新的解。另一方面，SK方程的群不变解是用经典的李群方法构造的。特别是，通过伽利略变换，以图形方式讨论了渐近可积方程的一些解析孤子-空心相互作用解。