### Abstract

With the help of energy analysis suggested by McLaughlin and Scott for the sine-Gordon equation, evolution of kink velocity modeling the propagation of a local conformational perturbation along the DNA molecule under the simultaneous action of dissipation effects and special nonstationary external fields is investigated. For a harmonically time-dependent external force, the kink velocity is characterized by oscillations about a rather monotonically decreasing trend expressed by an explicit analytical formula. The trend velocity coincides with the results of calculations of the kink velocity averaged over the period on different time intervals. Similar results are obtained for a nonstationary force in the form of a step function. A numerical analysis, in particular, demonstrates that the trend velocity changes its behavior for certain values of rectangular pulse duration.

Original language | English |
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Pages (from-to) | 89-98 |

Number of pages | 10 |

Journal | Russian Physics Journal |

Volume | 51 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2008 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Kink velocity in nonstationary external fields for the sine-Gordon model with allowance for dissipation effects.** / Krasnobaeva, L. A.; Shapovalov, A. V.

Research output: Contribution to journal › Article

*Russian Physics Journal*, vol. 51, no. 1, pp. 89-98. https://doi.org/10.1007/s11182-008-9020-7

}

TY - JOUR

T1 - Kink velocity in nonstationary external fields for the sine-Gordon model with allowance for dissipation effects

AU - Krasnobaeva, L. A.

AU - Shapovalov, A. V.

PY - 2008/1

Y1 - 2008/1

N2 - With the help of energy analysis suggested by McLaughlin and Scott for the sine-Gordon equation, evolution of kink velocity modeling the propagation of a local conformational perturbation along the DNA molecule under the simultaneous action of dissipation effects and special nonstationary external fields is investigated. For a harmonically time-dependent external force, the kink velocity is characterized by oscillations about a rather monotonically decreasing trend expressed by an explicit analytical formula. The trend velocity coincides with the results of calculations of the kink velocity averaged over the period on different time intervals. Similar results are obtained for a nonstationary force in the form of a step function. A numerical analysis, in particular, demonstrates that the trend velocity changes its behavior for certain values of rectangular pulse duration.

AB - With the help of energy analysis suggested by McLaughlin and Scott for the sine-Gordon equation, evolution of kink velocity modeling the propagation of a local conformational perturbation along the DNA molecule under the simultaneous action of dissipation effects and special nonstationary external fields is investigated. For a harmonically time-dependent external force, the kink velocity is characterized by oscillations about a rather monotonically decreasing trend expressed by an explicit analytical formula. The trend velocity coincides with the results of calculations of the kink velocity averaged over the period on different time intervals. Similar results are obtained for a nonstationary force in the form of a step function. A numerical analysis, in particular, demonstrates that the trend velocity changes its behavior for certain values of rectangular pulse duration.

UR - http://www.scopus.com/inward/record.url?scp=48349130102&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=48349130102&partnerID=8YFLogxK

U2 - 10.1007/s11182-008-9020-7

DO - 10.1007/s11182-008-9020-7

M3 - Article

AN - SCOPUS:48349130102

VL - 51

SP - 89

EP - 98

JO - Russian Physics Journal

JF - Russian Physics Journal

SN - 1064-8887

IS - 1

ER -