N=1超对称Sinh-Gordon的Backlund变换的可置换性

关于非对称四元方程贝克隆变换的Bianchi置换

On Bianchi permutability of Bäcklund transformations for asymmetric quad-equations

证明了非对称四元方程的贝克隆变换的Bianchi置换性（叠加原理的存在性）.这样的方程和贝克隆变换形成先验不同方程的三维相容系统。我们使用4D一致系统的四方程，通过双二次模式的结构的见解和考虑超一致的八元组的四方程装饰立方体进行证明。

Common Hirota Form Bäcklund Transformation for the Unified Soliton System

We study to unify soliton systems, KdV/mKdV/sinh-Gordon, through SO(2,1) $\cong$ GL(2,$\mathbb R$) $\cong$ Möbius group point of view, which might be a keystone to exactly solve some special non-linear differential equations. If we construct the $N$-soliton solutions through the KdV type Bäcklund transformation, we can transform different KdV/mKdV/sinh-Gordon equations and the Bäcklund transformations of the standard form into the same common Hirota form and the same common Bäcklund transformation except the equation which has the time-derivative term. The difference is only the time-dependenc…

Backlund transformation of the Geng-Xue system

We construct a Backlund transformation for the Geng-Xue system with the help of reciprocal and gauge transformations. Furthermore, we derive N-Backlund transformation for the Geng-Xue system resorting to Bianchi's permutability. As an application, we obtain some exact solutions of the Geng-Xue system including multi-kink, bell-shaped soliton. Finally, we discuss Backlund transformations for the Degasperis-Procesi and the Novikov equations, which are two reductions of the Geng-Xue system.

N=1超sinh-Gordon模型的II型超Backlund变换和可积缺陷

Type-II super-Backlund transformation and integrable defects for the N=1 super sinh-Gordon model

构造了N=1超对称sinh-Gordon方程的一个新的超Backlund变换.基于这个结构，我们提出了一个II型可积亏损的超对称sinh戈登模型符合这个新的转换，通过拉格朗日形式主义。计算了修正后的守恒能量、动量和超荷的显式表达式。此外，我们表明，该模型的II型缺陷也可以被视为一对融合缺陷的先前引入的类型。相关的缺陷矩阵的显式推导也作为一个必要条件的可积性的模型。

参量耦合Korteweg-de Vries系统的贝克隆变换多孤子解

Multisolitonic solutions from a Bäcklund transformation for a parametric coupled Korteweg-de Vries system

我们引入了一个参数耦合KdV系统，它包含，对于特定的参数值，KdV方程的复扩张和Hirota-Satsuma可积系统之一。我们得到了广义Gardner变换，并从相应的$\varepsilon$变形系统得到了参数耦合系统的守恒量的无穷序列。我们还得到了系统的贝克隆变换。我们证明了相关的置换定理对应于这样的转换，我们产生新的多孤子和周期解的系统依赖于几个参数。我们证明了在很宽的参数范围内，由置换定理得到的解都是正则解。最后，我们发现了新的多孤子解在一个非平凡的规则静态背景上的传播。

带亏损的经典可积超sinh-Gordon方程

Classical Integrable Super sinh-Gordon equation with defects

在Lagrange形式和Backlund变换下讨论了N=1超sinh-Gordon模型中缺陷的引入.修正的守恒动量和能量构造这种情况下。讨论了不同Backlund孤子解的一些显式例子。在由缺陷分裂的空间内的Lax公式导致了模型的可积性，并由此导致了无穷多个运动常数的存在