An exact solution for polaron in the nonlinear lattice in the Su–Schrieffer–Heeger approximation

Abstract

The exact solution for a polaron in a lattice with cubic nonlinearity is obtained. The electron–phonon interaction is taken into account in the Su–Schrieffer–Heeger approximation. The system of nonlinear differential equations in partial derivatives, obtained in the continuum approximation, is exactly integrable at a certain ratio between the parameters of nonlinearity, α, and the electron–phonon interaction, χ. An approximate solution is obtained for arbitrary values of α and χ. A good agreement between the analytical results with the numerical simulation is observed at not too large values of parameters α and χ, where the continuum approximation is valid. Stable solutions also exist at higher values of these parameters.