Soliton-like bipolaron in two-dimensional deformable electron-phonon system

Based on Emin's idea of deformation potential in deformable continuum, a bipolaron Hamiltonian is generalized to two-dimensional deformable electron-phonon system with the assumption of localized deformation potential of delta function. The dynamic properties of bipolaron are studied in the framework of Davydov's soliton theory, and a nonlinear Schrodinger equation is derived using the principle of least action. By function-series method, an exact two-dimensional (2D) soliton solution is obtained. We find that the center-of-mass motion of bipolaron is shown in a solitary wave form, and its relative motion is a harmonic one.