https://doi.org/10.1007/PL00011097
Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation
Institute of Physics and Astronomy () ,
University of Aarhus, 8000, Aarhus C, Denmark
and
NORDITA, Blegdamsvej 17, 2100, Copenhagen Ø, Denmark
Corresponding author: a fogedby@ifa.au.dk
Received:
8
November
2000
Published online: 15 March 2001
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.
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
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2001
