### Abstract

A linear equation associated with nonlinear wave equations which support solitons is analyzed. A complete set of solutions of this linear equation is described through the techniques of scattering theory. This set is used to construct an explicit representation of a Green's function for perturbation theory. The cases of the nonlinear Schrödinger and sine-Gordon equations are discussed in some detail.

Original language | English (US) |
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Pages (from-to) | 2008-2013 |

Number of pages | 6 |

Journal | Journal of Mathematical Physics |

Volume | 18 |

Issue number | 10 |

DOIs | |

State | Published - 1976 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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## Cite this

Keener, J. P., & McLaughlin, D. W. (1976). A Green's function for a linear equation associated with solitons.

*Journal of Mathematical Physics*,*18*(10), 2008-2013. https://doi.org/10.1063/1.523174