### Abstract

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 language | English (US) |
---|---|

Pages (from-to) | 1035-1046 |

Number of pages | 12 |

Journal | Journal of Experimental and Theoretical Physics |

Volume | 86 |

Issue number | 5 |

State | Published - May 1998 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Journal of Experimental and Theoretical Physics*,

*86*(5), 1035-1046.

**Optical solitons and quasisolitons.** / Zakharov, Vladimir E; Kuznetsov, E. A.

Research output: Contribution to journal › Article

*Journal of Experimental and Theoretical Physics*, vol. 86, no. 5, pp. 1035-1046.

}

TY - JOUR

T1 - Optical solitons and quasisolitons

AU - Zakharov, Vladimir E

AU - Kuznetsov, E. A.

PY - 1998/5

Y1 - 1998/5

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0042724273&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042724273&partnerID=8YFLogxK

M3 - Article

VL - 86

SP - 1035

EP - 1046

JO - Journal of Experimental and Theoretical Physics

JF - Journal of Experimental and Theoretical Physics

SN - 1063-7761

IS - 5

ER -