# soliton

A soliton is a non-linear object which moves through space without dispersion at constant speed. They occur naturally as solutions to the Korteweg - de Vries equation. They were first observed by John Scott Russell in the 19th century and then by Martin Kruskal and Norman Zabusky (who coined the term soliton) in a famous computer simulation in 1965. Insight into solitons can be obtained by noting that the Korteweg - de Vries equation satisfies D’Alembert’s solution:

$$u(x,t)=f(x-ct)+g(x+ct)$$ |

We see at once that this satisfies two important criteria: it has a constant velocity $c$, and it can also be shown that the two functions $f$ and $g$ can collide without altering shape. Solitons also occur in non-linear optics and as solutions to field equations in quantum field theory.

Title | soliton |
---|---|

Canonical name | Soliton |

Date of creation | 2013-03-22 17:47:50 |

Last modified on | 2013-03-22 17:47:50 |

Owner | invisiblerhino (19637) |

Last modified by | invisiblerhino (19637) |

Numerical id | 10 |

Author | invisiblerhino (19637) |

Entry type | Definition |

Classification | msc 35Q51 |

Classification | msc 37K40 |

Synonym | solitary wave |