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Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation |
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| Authors: | HC Fogedby |
| Institution: | Institute of Physics and Astronomy, University of Aarhus, 8000, Aarhus C, Denmark and NORDITA, Blegdamsvej 17, 2100, Copenhagen ?, Denmark, DK |
| 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. Received 8 November 2000 |
| 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 |
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