Integrability and exact solutions of a two-component Korteweg-de Vries system

In the present paper, the prolongation technique and Painlevé analysis are performed to a two-component Korteweg-de Vries system. It is proved that this system is both Lax integrable and P-integrable. By embedding the prolongation algebra in the sl(3;C) algebra, the 3×3 Lax representation of the system is derived. Moreover, the auto-Bäcklund transformation and some exact solutions for the two-component Korteweg-de Vries system are proposed explicitly, and it is shown that this system owns solitary wave solutions which demonstrate fission and fusion behaviors.