Integrability aspects of some two-component KdV systems

Some two-component Korteweg-de Vries systems are studied by prolongation technique and Painlevé analysis. Especially, the two-component KdV system conjectured to be integrable by Foursov is proved to be both Lax integrable and P-integrable. Its conservation laws are investigated based on the obtained Lax pair. Furthermore, it is shown that the three two-component Korteweg-de Vries systems are identical under certain invertible linear transformations. Finally, the auto-Bäcklund transformation and some exact solutions for the two-component Korteweg-de Vries system are derived explicitly.