# Graduate School in Nonlinear Science

### Sponsored by the Danish Research Academy

** Optical Solitons and Quasisolitons**

by E.A.Kuznetsov

Landau Institute for Theoretical Physics

Moscow

Russia

e-mail: kuznetso@itp.ac.ru

**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.