论文标题
（2+1） - 二维sawada-kotera方程的多个孤子解决方案的新层次结构
New hierarchy of multiple soliton solutions for the (2+1)-dimensional Sawada-Kotera equation
论文作者
论文摘要
A new transformation $u=4 ({\rm ln}f)_x$ that can formulate a quintic linear equation and a pair of Hirota's bilinear equations for the (2+1)-dimensional Sawada-Kotera (2DSK) equation is reported firstly, which enables one to obtain a new hierarchy of multiple soliton solutions of the 2DSK equation.它表明了一个至关重要的事实，即非线性偏微分方程可能具有两个孤子解决方案的两个层次结构，而2DSK方程是本文中的第一个也是唯一的。 Quintic线性方程是通过一对Hirota的双线性方程来求解的，其中一个是（2+1） - 二维双线性SK方程，由$ u = 2（{\ rm ln} f）_ {x} $获得，而另一个是双线性kdv kdv equaration。 （1+1） - 维度SK方程不具有此属性。作为另一个示例，具有一对Hirota的双线性方程的A（3+1） - 二维非线性偏微分方程，但是仅研究了一个层次层次结构。
A new transformation $u=4 ({\rm ln}f)_x$ that can formulate a quintic linear equation and a pair of Hirota's bilinear equations for the (2+1)-dimensional Sawada-Kotera (2DSK) equation is reported firstly, which enables one to obtain a new hierarchy of multiple soliton solutions of the 2DSK equation. It tells a crucial fact that a nonlinear partial differential equation could possess two hierarchies of multiple soliton solutions and the 2DSK equation is the first and only one found in this paper. 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 by $u=2 ({\rm ln}f)_{x}$, 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 hierarchy of multiple soliton solutions is studied.
