### Abstract

We present an alternative method for the calculation of the interaction between spirals in oscillatory media. This method is based on a rigorous evaluation of the perturbation of an isolated spiral resulting from neighboring spirals in a linear approximation. For the complex Ginzburg-Landau equation, the existence of bound states is identified with the parameter range where the perturbations behave in an oscillatory manner. The results for the equilibrium distance for two spirals in the bound state and also the dependence of the velocity of the spiral on the distance are in good agreement with numerical simulations. In the equally charged case, we find multiple bound states which may be interpreted as multiply armed spirals. Outside the oscillatory range, well-separated spirals appear to repel each other regardless of topological charge.

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

Pages (from-to) | 3231-3241 |

Number of pages | 11 |

Journal | Physical Review E |

Volume | 47 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 1993 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)

### Cite this

*Physical Review E*,

*47*(5), 3231-3241. https://doi.org/10.1103/PhysRevE.47.3231

}

*Physical Review E*, vol. 47, no. 5, pp. 3231-3241. https://doi.org/10.1103/PhysRevE.47.3231

**Theory of interaction and bound states of spiral waves in oscillatory media.** / Aronson, Igor; Kramer, Lorenz; Weber, Andreas.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Theory of interaction and bound states of spiral waves in oscillatory media

AU - Aronson, Igor

AU - Kramer, Lorenz

AU - Weber, Andreas

PY - 1993/1/1

Y1 - 1993/1/1

N2 - We present an alternative method for the calculation of the interaction between spirals in oscillatory media. This method is based on a rigorous evaluation of the perturbation of an isolated spiral resulting from neighboring spirals in a linear approximation. For the complex Ginzburg-Landau equation, the existence of bound states is identified with the parameter range where the perturbations behave in an oscillatory manner. The results for the equilibrium distance for two spirals in the bound state and also the dependence of the velocity of the spiral on the distance are in good agreement with numerical simulations. In the equally charged case, we find multiple bound states which may be interpreted as multiply armed spirals. Outside the oscillatory range, well-separated spirals appear to repel each other regardless of topological charge.

AB - We present an alternative method for the calculation of the interaction between spirals in oscillatory media. This method is based on a rigorous evaluation of the perturbation of an isolated spiral resulting from neighboring spirals in a linear approximation. For the complex Ginzburg-Landau equation, the existence of bound states is identified with the parameter range where the perturbations behave in an oscillatory manner. The results for the equilibrium distance for two spirals in the bound state and also the dependence of the velocity of the spiral on the distance are in good agreement with numerical simulations. In the equally charged case, we find multiple bound states which may be interpreted as multiply armed spirals. Outside the oscillatory range, well-separated spirals appear to repel each other regardless of topological charge.

UR - http://www.scopus.com/inward/record.url?scp=6244299076&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=6244299076&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.47.3231

DO - 10.1103/PhysRevE.47.3231

M3 - Article

AN - SCOPUS:6244299076

VL - 47

SP - 3231

EP - 3241

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 5

ER -