= Complex Ginzburg–Landau equation
= cGLE
{c}
{synonym}
The <complex Ginzburg–Landau equation> is a nonlinear complex-amplitude evolution equation with linear and cubic terms and generally complex coefficients. The driven-condensate form $\Psi_t=(\alpha-\beta|\Psi|^2)\Psi+i(\nabla^2-g|\Psi|^2+s)\Psi$ has gain/loss coefficients $\alpha,\beta$ and conservative interaction/frequency coefficients $g,s$. A uniform nonzero state has <number density> $\alpha/\beta$ when $\alpha,\beta>0$.
A <complex Ginzburg–Landau equation> describes a <complex number> disturbance amplitude through linear amplification, <advection>, complex <diffusion equation> terms, and often <cubic amplitude saturation>. A constant-coefficient example is $\psi_t+U\psi_x=\mu\psi+(1+ic_d)\psi_{xx}-|\psi|^2\psi$. Here real $U,\mu,c_d$ describe transport, linear <growth rate> and dispersive <diffusion equation> terms. Omitting the cubic term gives the <linear complex Ginzburg-Landau equation>.
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