Invariants of nonlinear propagation of femtosecond pulses

The author, V. A. Trofimov and his colleagues propose the transformation of the equation describing the propagation of femtosecond pulses with allowance for the dispersion of nonlinear response and linear dispersion of the second and third orders, which allows them to write the equation in a form convenient for numerical modeling. On the basis of this transformation, we obtain the invariants of nonlinear propagation containing information on the pulse phase. Some of the invariants obtained contain no information on the nonlinear addition to the permittivity of a transparent medium. The invariants obtained can be used for both checking the results of numerical experiments and analysis of interaction of the femtosecond pulse with the material.