Soliton-Like Bi-plasma Polaron

In the framework of phonon-plasmon cooperative effect mechanism, the differential equation for the wavefunction of the travelling soliton-like bi-plasma polaron (BPP) is derived. Then it is proven that the solution can be simply one-dimensional form. Meanwhile, the velocity range of the travelling soliton-like BPP is studied, thereby, we found that the quantity of the materials, where the travelling soliton-like BPP can exist, should be very small, i.e. . This result is consistent with the recently reported ones. Finally, an analytic approximation solution is given.