A new transformation $v=4{\left(\ln f\right)}_{xx}$ that can formulate a quintic linear equation and a pair of Hirota’s bilinear equations for the (2 + 1)-dimensional Sawada–Kotera (2DSK) Eq. (1) or $u=4{\left(\ln f\right)}_x$ for 2DSK Eq. (2) is reported firstly, which enables one to obtain a new set of multiple soliton solutions of the 2DSK equation. They are not special cases of the known multiple solitons. The results presented in this paper show that the 2DSK equation not only possesses two sets of multiple soliton solutions, but also has a relation between them that the square of $f_n$ in $n$-soliton solution $u=4{\left(\ln f_n\right)}_x$ can also be obtained from the singularity limit of $f_{2n}$ in $2n$-soliton solution $u=2{\left(\ln f_{2n}\right)}_x$ by using dual combination rules and a singular limit method. This property is unusual and the 2DSK equation is the first and only one found so far by us. Also, it establishes a connection of two equations because the quintic linear equation is solved by a pair of Hirota’s bilinear equations, of which one is the (2 + 1)-dimensional bilinear SK equation obtained under the case $u=2{\left(\ln f\right)}_x,$ and the other is the bilinear KdV equation. The (1 + 1)-dimensional SK equation does not possess this property. As another example, a (3 + 1)-dimensional nonlinear partial differential equation possessing a pair of Hirota’s bilinear equations, however only bearing one set of multiple soliton solutions is studied.

新的转变 $v=4{（\ln F）}_{XX}$可以为（2 + 1）维Sawada-Kotera（2DSK）方程式表达一个五次线性方程式和一对Hirota双线性方程式。（1）或$ü=4{（\ln F）}_X$适用于2DSK式 首先报道了（2），这使得一个人可以获得一组新的2DSK方程的多个孤子解。它们不是已知的多孤子的特殊情况。本文给出的结果表明，2DSK方程不仅具有两组多重孤子解，而且它们之间的关系是：$F_{ñ}$ 在 $ñ$-孤子解 $ü=4{（\ln F_{ñ}）}_X$ 也可以从奇异极限得到 $F_{\mathrm{2个}ñ}$ 在 $\mathrm{2个}ñ$-孤子解 $ü=\mathrm{2个}{（\ln F_{\mathrm{2个}ñ}）}_X$通过使用双重组合规则和奇异极限方法。此属性是不寻常的，到目前为止，我们发现的第一个也是唯一的一个是2DSK方程。此外，由于五对线性方程式是由一对Hirota双线性方程式求解的，所以它建立了两个方程式的连接，其中一个是在这种情况下获得的（2 + 1）维双线性SK方程式。$ü=\mathrm{2个}{（\ln F）}_X，$另一个是双线性KdV方程。（1 +1）维SK方程不具有此属性。作为另一个示例，具有一对Hirota双线性方程组的（3 +1）维非线性偏微分方程，但是仅研究一组多重孤子解。