Stable localized solutions of arbitrary length for the quintic Swift-Hohenberg equation

Hidetsugu Sakaguchi, Helmut R. Brand

    Research output: Contribution to journalArticle

    89 Citations (Scopus)

    Abstract

    We show that localized solutions of arbitrary length are stable over a finite parameter interval of subcritical values for the quintic Swift-Hohenberg equation with a destabilizing cubic term. This equation is thought to model a weakly hysteretic transition to stationary patterns. We argue that the stabilization of the localized states of arbitrary length can be traced back to the interaction between long wavelength modulations and spatial variations on the length scale of one unit cell. These results are critically compared with other known mechanisms to stabilize localized states in various situations. We also discuss for which experimental systems the states predicted here could be detected including e.g. the stationary onset of binary fluid convection.

    Original languageEnglish
    Pages (from-to)274-285
    Number of pages12
    JournalPhysica D: Nonlinear Phenomena
    Volume97
    Issue number1-3
    DOIs
    Publication statusPublished - Jan 1 1996

    All Science Journal Classification (ASJC) codes

    • Statistical and Nonlinear Physics
    • Mathematical Physics
    • Condensed Matter Physics
    • Applied Mathematics

    Fingerprint Dive into the research topics of 'Stable localized solutions of arbitrary length for the quintic Swift-Hohenberg equation'. Together they form a unique fingerprint.

  • Cite this