Complexiton solutions of the mKdV equation with self-consistent sources

A class of complexiton solutions of the mKdV equation with self-consistent sources (mKdVESCSs) are presented by the generalized binary Darboux transformation (GBDT) with N arbitrary t-functions. Taking the special initial seed solution for auxiliary linear problems and the special functions of time t, the real-valued 1-complexiton solution of the mKdVESCSs is considered through the GBDT by selecting the complex spectral parameters in its Lax pair. It is important to point out that the real-valued 1-complexiton solution of the mKdVESCSs is analytical and singular. Moreover, the detailed structures of the 1-complexiton solution are given out analytically and graphically.