Extreme nonlinear optics in a Kerr medium: Exact soliton solutions for a few cycles

Exact soliton solutions containing only a few cycles are found within the framework of a nonlinear full wave equation in a Kerr medium. It is proven numerically that they are stable and play a fundamental role in the pulse propagation dynamics. These wave solitons cover the range from the fundamental Schrodinger solitons, which occur for long pulses involving many field oscillations, to extremely short pulses, which contain only one optical period