Born-Infeld-type phantom on the brane world

We study the evolution of a Born-Infeld (BI) type phantom in the second Randall-Sundrum brane world scenario, and find that an attractor solution exists for the potential with a maximum, which implies a cosmological constant at late time. Especially, we discuss the BI model of the constant potential without and with dust matter. In the weak tension limit of the brane, we obtain an exact solution for the BI phantom and scale factor and show that there is no big rip during the evolution of the brane.