Optical solitons and quasisolitons

V. E. Zakharov, E. A. Kuznetsov

Research output: Contribution to journalArticlepeer-review

104 Scopus citations


Optical solitons and quasisolitons are investigated in reference to Cherenkov radiation. It is shown that both solitons and quasisolitons can exist, if the linear operator specifying their asymptotic behavior at infinity is sign-definite. In particular, the application of this criterion to stationary optical solitons shifts the soliton carrier frequency at which the first derivative of the dielectric constant with respect to the frequency vanishes. At that point the phase and group velocities 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 based on the boundedness of the Hamiltonian for a fixed value of the pulse energy.

Original languageEnglish (US)
Pages (from-to)1035-1046
Number of pages12
JournalJournal of Experimental and Theoretical Physics
Issue number5
StatePublished - May 1998

ASJC Scopus subject areas

  • General Physics and Astronomy


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