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Motion of spiral waves in the complex Ginzburg-Landau equation

Publication ,  Journal Article
Aguareles, M; Chapman, SJ; Witelski, T
Published in: Physica D: Nonlinear Phenomena
April 1, 2010

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered. For parameters close to the vortex limit, and for a system of spiral waves with well-separated centres, laws of motion of the centres are found which vary depending on the order of magnitude of the separation of the centres. In particular, the direction of the interaction changes from along the line of centres to perpendicular to the line of centres as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wavenumber and frequency are determined. These depend on the positions of the centres of the spirals, and so evolve slowly as the spirals move. © 2009 Elsevier B.V.

Duke Scholars

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

April 1, 2010

Volume

239

Issue

7

Start / End Page

348 / 365

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Aguareles, M., Chapman, S. J., & Witelski, T. (2010). Motion of spiral waves in the complex Ginzburg-Landau equation. Physica D: Nonlinear Phenomena, 239(7), 348–365. https://doi.org/10.1016/j.physd.2009.12.003
Aguareles, M., S. J. Chapman, and T. Witelski. “Motion of spiral waves in the complex Ginzburg-Landau equation.” Physica D: Nonlinear Phenomena 239, no. 7 (April 1, 2010): 348–65. https://doi.org/10.1016/j.physd.2009.12.003.
Aguareles M, Chapman SJ, Witelski T. Motion of spiral waves in the complex Ginzburg-Landau equation. Physica D: Nonlinear Phenomena. 2010 Apr 1;239(7):348–65.
Aguareles, M., et al. “Motion of spiral waves in the complex Ginzburg-Landau equation.” Physica D: Nonlinear Phenomena, vol. 239, no. 7, Apr. 2010, pp. 348–65. Scopus, doi:10.1016/j.physd.2009.12.003.
Aguareles M, Chapman SJ, Witelski T. Motion of spiral waves in the complex Ginzburg-Landau equation. Physica D: Nonlinear Phenomena. 2010 Apr 1;239(7):348–365.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

April 1, 2010

Volume

239

Issue

7

Start / End Page

348 / 365

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics