(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2013) Amiranashvili, Shalva; Bandelow, Uwe; Akhmediev, Nail
We consider the propagation of ultrashort optical pulses in nonlinear
fibers and suggest a new theoretical framework for the description of pulse
dynamics and exact characterization of solitary solutions. Our approach deals
with a proper complex generalization of the nonlinear Maxwell equations and
completely avoids the use of the slowly varying envelope approximation. The
only essential restriction is that fiber dispersion does not favor both the
so-called Cherenkov radiation, as well as the resonant generation of the
third harmonics, as these effects destroy ultrashort solitons. Assuming that
it is not the case, we derive a continuous family of solitary solutions
connecting fundamental solitons to nearly single-cycle ultrashort ones for
arbitrary anomalous dispersion and cubic nonlinearity.
