A gradient expansion is used to obtain a Lyapunov functional (the nonequilibrium potential) for the supercritical complex Ginzburg-Landau equation. The method simplifies the task of solving the Hamilton-Jacobi equation associated with the steady-state distribution of the stochastic Ginzburg-Landau equation with weak noise and it confirms and extends results obtained previously by a more tedious calculation. The method opens the possibility for studying other situations not yet explored.
|Number of pages||7|
|Journal||Physics Letters, Section A: General, Atomic and Solid State Physics|
|State||Published - 26 Oct 1992|
Bibliographical noteFunding Information:
WewouldliketothankT.TelandE.Tirapeguiforusefuldiscussions. ThisworkwassupportedbytheDeutsche Forschungsgemeinschaft through the Sonderforschungsbereich 237 Unordnung und grol3e Fluktuationen. One of us (O.D.) wishes to thank the Deutscher Akademischer Austauschsdienst for financial support.