Graduate School in Nonlinear Science

Sponsored by the Danish Research Academy

Optical Solitons and Quasisolitons

by E.A.Kuznetsov
Landau Institute for Theoretical Physics

Friday January 16, 1998, 10.00 h
at OFD, Meeting Room, Building 128, Risø

Abstract: Optical solitons and quasisolitons are examined relative to Cherenkov radiation. It is shown that both solitons and quasisolitons can exist if the linear operator defining their asymptotics at infinity is sign definite. In particular, application of this criterion to the stationary optical solitons yields the soliton carrying frequency where the first derivative of the dielectric permittivity vanishes. At this point the phase and group velocities coincide. Both solitons and quasisolitons are absent if the third order dispersion is taken into account. By means of the sign definiteness of the operator and by using the integral estimations of the Sobolev type the soliton stability is established for the fourth order dispersion. This proof is based on the boundedness of the Hamiltonian for fixed pulse power.