WIAS Preprint No. 1514, (2010)

Relative stability of multipeak localized patterns


Authors

  • Vladimirov, Andrei G.
    ORCID: 0000-0002-7540-8380
  • Lefever, René
  • Tlidi, Mustapha
    ORCID: 0000-0003-3660-2524

2010 Mathematics Subject Classification

  • 35B99 37L15

2008 Physics and Astronomy Classification Scheme

  • 45.70.Qj 05.45.-a 42.65.Pc

Keywords

  • Localized structures, Lyapunov functional, stability

DOI

10.20347/WIAS.PREPRINT.1514

Abstract

We study relative stability properties of different clusters of closely packed one- and two-dimensional localized peaks of the Swift-Hohenberg equation. We demonstrate the existence of a 'spatial Maxwell' point where clusters are almost equally stable, irrespective of the number of pes involved. Above (below) the Maxwell point, clusters become more (less) stable with the increase of the number of peaks.

Appeared in

  • Phys. Rev. A, 84 (2011) pp. 043848/1--043848/4.

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