The N-soliton solutions for the modified KdV equation with self-consistent sources

The N-soliton solutions for the modified KdV equation with self-consistent sources are obtained through Hirota's method and Wronskian technique respectively. Some novel determinantal identities are presented to treat the nonlinear term in the time evolution and finish the Wronskian verifications. The uniformity of these two kinds of N-soliton solutions is proved.