### Abstract

In this work, we study the persistence of a homoclinic orbit of the sine-Gordon equation under diffusive and driven perturbations. An analytic perturbation method based on time-dependent scattering theory, together with Fredholm theory, is used to establish persistence. The estimates are given in space-time function spaces, with a certain time decay required for the existence of a homoclinic orbit.

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

Pages (from-to) | 283-299 |

Number of pages | 17 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 53 |

Issue number | 3 |

State | Published - Mar 2000 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*53*(3), 283-299.

**Homoclinic orbits for the perturbed sine-Gordon equation.** / Shatah, Jalal; Zeng, Chongchun.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 53, no. 3, pp. 283-299.

}

TY - JOUR

T1 - Homoclinic orbits for the perturbed sine-Gordon equation

AU - Shatah, Jalal

AU - Zeng, Chongchun

PY - 2000/3

Y1 - 2000/3

N2 - In this work, we study the persistence of a homoclinic orbit of the sine-Gordon equation under diffusive and driven perturbations. An analytic perturbation method based on time-dependent scattering theory, together with Fredholm theory, is used to establish persistence. The estimates are given in space-time function spaces, with a certain time decay required for the existence of a homoclinic orbit.

AB - In this work, we study the persistence of a homoclinic orbit of the sine-Gordon equation under diffusive and driven perturbations. An analytic perturbation method based on time-dependent scattering theory, together with Fredholm theory, is used to establish persistence. The estimates are given in space-time function spaces, with a certain time decay required for the existence of a homoclinic orbit.

UR - http://www.scopus.com/inward/record.url?scp=0034406879&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034406879&partnerID=8YFLogxK

M3 - Article

VL - 53

SP - 283

EP - 299

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 3

ER -