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We investigate the polaron dynamics on the nonlinear lattice with the cubic nonlinearity in the tight-binding approximation. The electron-phonon interaction is accounted in the Su-Schrieffer-Heeger approximation. The system of nonlinear partial differential equations is derived in the continuum approximation. It has an exact solution at a special relation between parameters of lattice nonlinearity α and electron-phonon interaction χ. An approximate analytical solution is obtained at arbitrary parameters α and χ. Results of the numeric simulations are in a good agreement with the analytical predictions in both cases. The range of parameter values, where theoretical formulae are valid, is determined.

The possible mechanism of charge transfer via polarons to long distances in biopolymers was con sidered. A set of accurately integrable equations was obtained for a lattice with a potential of interaction of neighboring particles with cubic nonlinearity and at a certain ratio of the parameters of the problem. This sys tem has many soliton solutions, while the polaron is a one soliton solution. Numerical modeling proved high stability of the obtained solutions. A new class of stable polarons with several peaks were detected for arbitrary values of the parameters. The behavior of polarons on a lattice with defects was studied by numerical meth ods. The applicability of the results to rationalization of recent experiments on the effective charge transfer in biopolymers was analyzed.

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