耿学系统的Backlund变换
Backlund transformation of the Geng-Xue system
摘要：
利用倒易变换和规范变换构造了耿-薛系统的Backlund变换。利用Bianchi的可置换性，我们得到了耿学系统的N-Backlund变换。作为应用，我们得到了含有多扭结钟形孤子的耿-薛系统的一些精确解。最后，我们讨论了Degasperis-Procesi方程和Novikov方程的Backlund变换，这两个方程是耿-薛系统的两个约化。
英文摘要：
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.
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