### Abstract

We describe the evolution of the envelope of a wavetrain which, at a critical value of the stress parameter, breaks the rotational symmetry of the governing equations. The new envelope equation is a generalization to wavelike disturbances of the Newell-Whitehead-Segel equation and the one-dimensional complex Ginzburg-Landau equation. The most novel prediction of the new theory is that spatially uniform envelopes are rarely stable and that the dynamics is dominated by terms which c...onserve phase space volume. In particular, it turns out that the strongest spatial modulation takes place along the wave crests, perpendicular to the direction of the propagation. We also discuss mean drift effects and in particular their consequences near lateral boundaries.

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

Pages (from-to) | 67-73 |

Number of pages | 7 |

Journal | Physics Letters A |

Volume | 118 |

Issue number | 2 |

DOIs | |

State | Published - Sep 29 1986 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters A*,

*118*(2), 67-73. https://doi.org/10.1016/0375-9601(86)90649-3

**Evolution of the order parameter in situations with broken rotational symmetry.** / Brand, Helmut R.; Lomdahl, Peter S.; Newell, Alan C.

Research output: Contribution to journal › Article

*Physics Letters A*, vol. 118, no. 2, pp. 67-73. https://doi.org/10.1016/0375-9601(86)90649-3

}

TY - JOUR

T1 - Evolution of the order parameter in situations with broken rotational symmetry

AU - Brand, Helmut R.

AU - Lomdahl, Peter S.

AU - Newell, Alan C

PY - 1986/9/29

Y1 - 1986/9/29

N2 - We describe the evolution of the envelope of a wavetrain which, at a critical value of the stress parameter, breaks the rotational symmetry of the governing equations. The new envelope equation is a generalization to wavelike disturbances of the Newell-Whitehead-Segel equation and the one-dimensional complex Ginzburg-Landau equation. The most novel prediction of the new theory is that spatially uniform envelopes are rarely stable and that the dynamics is dominated by terms which c...onserve phase space volume. In particular, it turns out that the strongest spatial modulation takes place along the wave crests, perpendicular to the direction of the propagation. We also discuss mean drift effects and in particular their consequences near lateral boundaries.

AB - We describe the evolution of the envelope of a wavetrain which, at a critical value of the stress parameter, breaks the rotational symmetry of the governing equations. The new envelope equation is a generalization to wavelike disturbances of the Newell-Whitehead-Segel equation and the one-dimensional complex Ginzburg-Landau equation. The most novel prediction of the new theory is that spatially uniform envelopes are rarely stable and that the dynamics is dominated by terms which c...onserve phase space volume. In particular, it turns out that the strongest spatial modulation takes place along the wave crests, perpendicular to the direction of the propagation. We also discuss mean drift effects and in particular their consequences near lateral boundaries.

UR - http://www.scopus.com/inward/record.url?scp=0039204506&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039204506&partnerID=8YFLogxK

U2 - 10.1016/0375-9601(86)90649-3

DO - 10.1016/0375-9601(86)90649-3

M3 - Article

AN - SCOPUS:0039204506

VL - 118

SP - 67

EP - 73

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 2

ER -