Polarons on nonlinear lattice in the Su-Schrieffer-Heeger approximation: Exact solution and multipeaked polarons

We investigate the polaron dynamics on the nonlinear lattice with the cubic nonlinearity. The electron-phonon interaction is accounted in the Su-Schrieffer-Heeger approximation. An exact analytical solution is obtained in the continuum approximation at certain relation of parameters. The numerical simulation agrees with analytics very well. Moreover, colliding polarons recover their shapes and velocities after the elastic collision suggesting that the solution belongs to the exactly integrable system. When the continuum approximation is invalid (parameters of nonlinearity and electron-phonon interaction are not small), a new family of stable multipeaked polarons is found. These polarons are formed by the coupled solitons hold together by the electron-phonon interaction.