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

H.C. Fogedby
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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

The European Physical Journal B: Condensed Matter and Complex Systems, 2001, vol. 20, issue 2, 153-156

Abstract: 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.

Keywords: PACS. 05.10.Gg Stochastic analysis methods (Fokker-Planck; Langevin; etc.) – 05.45.-a Nonlinear dynamics and nonlinear dynamical systems – 64.60.Ht Dynamic critical phenomena – 05.45.Yv Solitons (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1007/PL00011097

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