The report is devoted to an analytical solution and computer simulation of the THG for femtosecond pulses taking into
account self- and cross- modulation of interacting waves. As it is well known, for the case under consideration because
of pulses self-action the low efficiency of frequency conversion takes place for phase and group wave matching as rule.
Therefore, in physical experiment, the THG is realized on the base of SHG and then summary frequency wave generation
for waves with basic and doubling frequencies. Using an original approach, we obtained an explicit solution of
Schrödinger equations describing THG in the framework of longer duration of pulses. It should be stressed, that the main
feature of our approach is an using of conservation laws for interacting waves. We found various regime of trebling frequency
and shown that under some conditions the THG process has a bistable features on conversion efficiency.
On the base of our solution we show an existence of two regimes: one of them corresponds to low frequency conversion
efficiency and other to high one. It is very important for practice realization that switching between two stable states can
be realized due to changing of phase mismatching in short intervals of its values. It should be noticed that computer
simulation results, which are obtained with taking into account second order dispersion and without it, has confirmed
analytical results. For computer simulation, we constructed conservative difference scheme, which gave a possibility to
made simulation with high accuracy.