OPTICAL SOLITONS AND QUASISOLITONS

Optical solitons and quasisolitons are investigated in reference to Ch erenkov radiation. It is shown that both solitons and quasisolitons ca n exist, if the linear operator specifying their asymptotic behavior a t infinity is sign-definite. In particular, the application of this cr iterion to stationary optical solitons shifts the soliton carrier freq uency at which the first derivative of the dielectric constant with re spect to the frequency vanishes. At that point the phase and group vel ocities coincide. Solitons and quasisolitons are absent, if the third- order dispersion is taken into account. The stability of a soliton is proved for fourth order dispersion using the sign-definiteness of the operator and integral estimates of the Sobolev type. This proof is bas ed on the boundedness of the Hamiltonian for a fixed value of the puls e energy. (C) 1998 American Institute of Physics. [S1063-7761(98)02405 -6].