### 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) |
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Pages (from-to) | 91-101 |

Number of pages | 11 |

Journal | Studies in Applied Mathematics |

Volume | 71 |

Issue number | 2 |

State | Published - Oct 1 1984 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Ercolani, N., Forest, M. G., & Mclaughlin, D. W. (1984). Modulational Stability of Two-Phase Sine-Gordon Wavetrains.

*Studies in Applied Mathematics*,*71*(2), 91-101.