Nonequilibrium potential for the Ginzburg-Landau equation in the phase-turbulent regime

Orazio Descalzi*, R. Graham

*Autor correspondiente de este trabajo

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

16 Citas (Scopus)

Resumen

The steady state distribution functional of the supercritical complex Ginzburg-Landau equation with weak noise is determined asymptotically for long-wave-length fluctuations including the phaseturbulent regime. This is done by constructuring a non-equilibrium potential solving the Hamilton-Jacobi equation associated with the Fokker-Planck equation. The non-equilibrium potential serves as a Lyapunov functional. In parameter space it consists of two branches which are joined at the Benjamin-Feir instability. In the Benjamins-Feir stable regime the non-equilibrium potential has minima in the plane-wave attractors and our result generalizes to arbitrary dimension an earlier result for one dimension. Beyond the Benjamin-Feir instability the potential in the function space has a minimum which is degererate with respects to arbirary long-wavelength phase variations. The dynamics on the minimum set obey the generalized Kuramoto-Sivashinsky equation.

Idioma originalInglés
Páginas (desde-hasta)509-513
Número de páginas5
PublicaciónZeitschrift für Physik B Condensed Matter
Volumen93
N.º4
DOI
EstadoPublicada - dic. 1994
Publicado de forma externa

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