### Abstract

The characterization of real, N phase, quasiperiodic solutions of the sine-Gordon equation has been an open problem. In this paper we achieve this result, employing techniques of classical algebraic geometry which have not previously been exploited in the soliton literature. A significant by-product of this approach is a natural algebraic representation of the full complex isospectral manifolds, and an understanding of how the real isospectral manifolds are embedded. By placing the problem in this general context, these methods apply directly to all soliton equations whose multiphase solutions are related to hyperelliptic functions.

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

Pages (from-to) | 1-49 |

Number of pages | 49 |

Journal | Communications in Mathematical Physics |

Volume | 99 |

Issue number | 1 |

DOIs | |

State | Published - Mar 1985 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*99*(1), 1-49. https://doi.org/10.1007/BF01466592

**The geometry of real sine-Gordon wavetrains.** / Ercolani, Nicholas M; Forest, M. Gregory.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 99, no. 1, pp. 1-49. https://doi.org/10.1007/BF01466592

}

TY - JOUR

T1 - The geometry of real sine-Gordon wavetrains

AU - Ercolani, Nicholas M

AU - Forest, M. Gregory

PY - 1985/3

Y1 - 1985/3

N2 - The characterization of real, N phase, quasiperiodic solutions of the sine-Gordon equation has been an open problem. In this paper we achieve this result, employing techniques of classical algebraic geometry which have not previously been exploited in the soliton literature. A significant by-product of this approach is a natural algebraic representation of the full complex isospectral manifolds, and an understanding of how the real isospectral manifolds are embedded. By placing the problem in this general context, these methods apply directly to all soliton equations whose multiphase solutions are related to hyperelliptic functions.

AB - The characterization of real, N phase, quasiperiodic solutions of the sine-Gordon equation has been an open problem. In this paper we achieve this result, employing techniques of classical algebraic geometry which have not previously been exploited in the soliton literature. A significant by-product of this approach is a natural algebraic representation of the full complex isospectral manifolds, and an understanding of how the real isospectral manifolds are embedded. By placing the problem in this general context, these methods apply directly to all soliton equations whose multiphase solutions are related to hyperelliptic functions.

UR - http://www.scopus.com/inward/record.url?scp=0001941143&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001941143&partnerID=8YFLogxK

U2 - 10.1007/BF01466592

DO - 10.1007/BF01466592

M3 - Article

AN - SCOPUS:0001941143

VL - 99

SP - 1

EP - 49

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1

ER -