= Benjamin-Feir instability
{c}
{title2=$1+c_1c_3<0$}
For the <complex Ginzburg–Landau equation> $A_t=A+(1+ic_1)A_{xx}-(1+ic_3)|A|^2A$, the uniform oscillation has a neutral <phase> mode whose <growth rate> is $\lambda=-(1+c_1c_3)k^2+O(k^4)$. Negative <phase> diffusion therefore causes a long-wavelength <modulational instability>. The <Benjamin-Feir stability condition> is the complementary positive-diffusion condition. On a finite domain an unstable wavenumber must actually be allowed by the boundary conditions.
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