### 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 sine-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) | 91-101 |

Number of pages | 11 |

Journal | Studies in Applied Mathematics |

Volume | 71 |

Issue number | 2 |

State | Published - Oct 1984 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Studies in Applied Mathematics*,

*71*(2), 91-101.

**MODULATIONAL STABILITY OF TWO-PHASE SINE-GORDON WAVETRAINS.** / Ercolani, Nicholas M; Forest, M. Gregory; McLaughlin, David W.

Research output: Contribution to journal › Article

*Studies in Applied Mathematics*, vol. 71, no. 2, pp. 91-101.

}

TY - JOUR

T1 - MODULATIONAL STABILITY OF TWO-PHASE SINE-GORDON WAVETRAINS.

AU - Ercolani, Nicholas M

AU - Forest, M. Gregory

AU - McLaughlin, David W.

PY - 1984/10

Y1 - 1984/10

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 sine-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 sine-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.

UR - http://www.scopus.com/inward/record.url?scp=0021502431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0021502431&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0021502431

VL - 71

SP - 91

EP - 101

JO - Studies in Applied Mathematics

JF - Studies in Applied Mathematics

SN - 0022-2526

IS - 2

ER -