Negaton, positon and complexiton solutions of the nonisospectral KdV equations with self-consistent sources

The negaton, positon, and complexiton solutions of the nonisospectral KdV equations with self-consistent sources (KdVESCSs) are obtained by the generalized binary Darboux transformation (GBDT) with N arbitrary t-functions. Taking the special initial seed solution for auxiliary linear problems, the negaton, positon, and complexiton solutions of the nonisospectral KdVESCSs are considered through the GBDT by selecting the negative, positive and complex spectral parameters. It is important to point out that these solutions of the nonisospectral KdVESCSs are analytical and singular. We also show differences between these solutions with singularities. Moreover, the detailed characteristics of these solutions with nonisospectral properties and sources effects are described through some figures.

► In this paper, we investigate the nonisospectral KdV equations with self-consistent sources (KdVESCSs).
► We obtained the negaton, positon, and complexiton solutions of these equations by GBDT.
► These solutions are shown to possess moving singularities and the amplitude and velocity of the solitary wave vary with time.