### Abstract

The statistical initial value problem for the envelope equation dw/dt minus gamma d**2w/dx**2 equals chi w- beta w**2w*; gamma , beta complex, is discussed. (The derivatives are both partial derivatives. ) It is shown that there exists an instability (stability) criterion which determines whether the system underlying the above equation achieves or does not achieve a monochromatic state.

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

Pages (from-to) | 441-456 |

Number of pages | 16 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 27 |

Issue number | 3 |

State | Published - Nov 1974 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*SIAM Journal on Applied Mathematics*,

*27*(3), 441-456.

**STABILITY CRITERION FOR ENVELOPE EQUATIONS.** / Lange, Charles G.; Newell, Alan C.

Research output: Contribution to journal › Article

*SIAM Journal on Applied Mathematics*, vol. 27, no. 3, pp. 441-456.

}

TY - JOUR

T1 - STABILITY CRITERION FOR ENVELOPE EQUATIONS.

AU - Lange, Charles G.

AU - Newell, Alan C

PY - 1974/11

Y1 - 1974/11

N2 - The statistical initial value problem for the envelope equation dw/dt minus gamma d**2w/dx**2 equals chi w- beta w**2w*; gamma , beta complex, is discussed. (The derivatives are both partial derivatives. ) It is shown that there exists an instability (stability) criterion which determines whether the system underlying the above equation achieves or does not achieve a monochromatic state.

AB - The statistical initial value problem for the envelope equation dw/dt minus gamma d**2w/dx**2 equals chi w- beta w**2w*; gamma , beta complex, is discussed. (The derivatives are both partial derivatives. ) It is shown that there exists an instability (stability) criterion which determines whether the system underlying the above equation achieves or does not achieve a monochromatic state.

UR - http://www.scopus.com/inward/record.url?scp=0016130226&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016130226&partnerID=8YFLogxK

M3 - Article

VL - 27

SP - 441

EP - 456

JO - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 3

ER -