[en] Numerically the delicate scale multipeak structures of the electrostatic solitary waves are found for the three-component (electron-positron-ion, i.e., EPI) plasmas. The complicated homoclinic phase portraits for this two-degree-of-freedom system are presented, which indicate that the system exhibits more abundant nonlinear phenomena. This finding is very useful to unveil the coherent dynamical behavior in laser-plasma interaction. It has an implication of electron acceleration by a laser with soliton wave mechanism. (paper)