Based on the method of coherent states, the nonlinear effects caused by the interaction between electrons and acoustic lattice vibrations in an anharmonic linear chains are investigated in the secolid-neighbour interaction approximation. While the continous limits of the equations of motion is considered self -consistently, the cubic anharmonicity of the deformable potential leads to a new nonlinear equation for the electronic orobability amolitute, which gives a new solitary solution in the form of hyperelliptic integral. This shows that besides the bell-solitons there also exists a second type of solitary excitation with the shape of a kink.