Few-cycle pulse in the medium consisting of symmetric and asymmetrical molecules.

Stationary quantum states of asymmetrical molecules have the permanent dipole moment.

The pulse electric field is described by the equation of Konno, Kameyama, and Sanuki.

The new solitonic modes of propagation of the half- and single-period pulses are found.

The simultaneous generation of soliton of the second and zero harmonics is analyzed.