Modulational Stability of Two-Phase Sine-Gordon Wavetrains

Nicholas Ercolani; M. Gregory Forest; David W. Mclaughlin

doi:10.1002/sapm198471291

Modulational Stability of Two-Phase Sine-Gordon Wavetrains

Nicholas Ercolani
, M. Gregory Forest
, David W. Mclaughlin

Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

A modulational stability analysis is presented for real, two-phase sine-Gordon wavetrains. Using recent results on the geometry of these real solutions, an invariant representation in terms of Abelian differentials is derived for the sine-Gordon modulation equations. The theory thus attains the same integrable features of the previously completed KdV and sinh-Gordon modulations. The twophase results are as follows: kink-kink trains are stable, while the breather trains and kink-radiation trains are unstable, to modulations.

Original language	English (US)
Pages (from-to)	97-101
Number of pages	5
Journal	Studies in Applied Mathematics
Volume	71
Issue number	2
DOIs	https://doi.org/10.1002/sapm198471291
State	Published - Oct 1 1984

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Applied Mathematics

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title = "Modulational Stability of Two-Phase Sine-Gordon Wavetrains",

abstract = "A modulational stability analysis is presented for real, two-phase sine-Gordon wavetrains. Using recent results on the geometry of these real solutions, an invariant representation in terms of Abelian differentials is derived for the sine-Gordon modulation equations. The theory thus attains the same integrable features of the previously completed KdV and sinh-Gordon modulations. The twophase results are as follows: kink-kink trains are stable, while the breather trains and kink-radiation trains are unstable, to modulations.",

author = "Nicholas Ercolani and Forest, \{M. Gregory\} and Mclaughlin, \{David W.\}",

note = "Publisher Copyright: {\textcopyright} 2015 Wiley Periodicals, Inc., A Wiley Company.",

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AU - Forest, M. Gregory

AU - Mclaughlin, David W.

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Y1 - 1984/10/1

N2 - A modulational stability analysis is presented for real, two-phase sine-Gordon wavetrains. Using recent results on the geometry of these real solutions, an invariant representation in terms of Abelian differentials is derived for the sine-Gordon modulation equations. The theory thus attains the same integrable features of the previously completed KdV and sinh-Gordon modulations. The twophase results are as follows: kink-kink trains are stable, while the breather trains and kink-radiation trains are unstable, to modulations.

AB - A modulational stability analysis is presented for real, two-phase sine-Gordon wavetrains. Using recent results on the geometry of these real solutions, an invariant representation in terms of Abelian differentials is derived for the sine-Gordon modulation equations. The theory thus attains the same integrable features of the previously completed KdV and sinh-Gordon modulations. The twophase results are as follows: kink-kink trains are stable, while the breather trains and kink-radiation trains are unstable, to modulations.

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Modulational Stability of Two-Phase Sine-Gordon Wavetrains

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