Soliton fission and fusion of a new two-component Korteweg–de Vries (KdV) equation

In this paper, the Painlevé test is performed for a new two-component Korteweg–de Vries (KdV) equation proposed by Foursov. It is shown that this equation passes the integrability test and is P-integrable. By means of the truncated singular expansion, some explicit solutions from the trivial zero solution are derived. The phenomena of soliton fission and fusion are studied in detail.