Generalized Darboux transformations for the KP equation with self-consistent sources
Generalized Darboux transformations for the KP equation with self-consistent sources
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DOI：
10.1088/0305-4470/37/28/006
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发表时间：
2004-06
期刊：
影响因子：
--
通讯作者：
Ting Xiao;Yunbo Zeng
中科院分区：
文献类型：
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作者：
Ting Xiao;Yunbo Zeng
在约束KP方程的框架内处理具有自洽源的KP方程。这为获得KPESCS的Lax表示提供了一种自然的方法。基于共轭Lax对，构造了KPESCS在时间t上具有任意函数的广义二元Darboux变换，与KP方程的二元Darboux变换相比，提供了两个不同程度的KPESCS之间的非自backlund变换。提出了n次重复广义二元达布变换的公式，使我们能够求出KPESCS的n孤子解和块解以及其他一些解。
The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we construct the generalized binary Darboux transformation with arbitrary functions in time t for the KPESCS which, in contrast to the binary Darboux transformation of the KP equation, provides a non-auto-Backlund transformation between two KPESCSs with different degrees. The formula for N-times repeated generalized binary Darboux transformation is proposed and enables us to find the N-soliton solution and lump solution as well as some other solutions of the KPESCS.