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Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation

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  • H.C. Fogedby

    (Institute of Physics and Astronomy, University of Aarhus, 8000, Aarhus C, Denmark and NORDITA, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark)

Abstract

We discuss the mode spectrum in both the deterministic and noisy Burgers equations in one dimension. Similar to recent investigations of vortex depinning in superconductors, the spectrum is given by a non-Hermitian eigenvalue problem which is related to a `quantum' problem by a complex gauge transformation. The soliton profile in the Burgers equation serves as a complex gauge field engendering a mode transmutation of diffusive modes into propagating modes and giving rise to a dynamical pinning of localized modes about the solitons.

Suggested Citation

  • H.C. Fogedby, 2001. "Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(2), pages 153-156, March.
    • Handle: RePEc:spr:eurphb:v:20:y:2001:i:2:d:10.1007_pl00011097
    DOI: 10.1007/PL00011097
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