Negaton and Positon solutions of the soliton equation with self-consistent sources

Details Negaton and Positon solutions of the soliton equation with self-consistent sources Negaton and Positon solutions of the soliton equation with self-consistent sources

2003-04-16

arxiv.org/abs/nlin/0304030v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

13 pages, Latex, no figues, to be published in J. Phys. A: Math. Gen

Scientific paper

10.1088/0305-4470/36/18/308

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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