Negaton and positon solutions of the soliton equation with self-consistent sources
Yunbo ZengDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of ChinaYijun ShaoDepartment of Mathematical Sciences, Tsinghua University, Beijing 100084, People's Republic of ChinaWeimin XueMathematical Department, Hong Kong Baptist University, Kowloon, Hong Kong, People's Republic of China
2003en
ABI
Abstract
The KdV equation with self-consistent sources (KdVES) is used as a model to illustrate the method. A generalized binary Darboux transformation (GBDT) with an arbitrary time-dependent function for the KdVES as well as the formula for $N$-times repeated GBDT are presented. This GBDT provides non-auto-B\"{a}cklund transformation between two KdV equations with different degrees of sources and enable us to construct more general solutions with $N$ arbitrary $t$-dependent functions. By taking the special $t$-function, we obtain multisoliton, multipositon, multinegaton, multisoliton-positon, multinegaton-positon and multisoliton-negaton solutions of KdVES. Some properties of these solutions are discussed.
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