= Bloch stability operator
{c}
{title2=$L(q)=e^{-iq\cdot x}Le^{iq\cdot x}$}
For a spatially periodic nonlinear pattern, a <linear stability> disturbance is written $e^{\lambda t+iq\cdot x}v(x)$ with $v$ periodic on the pattern cell. The conjugated operator $L(q)$ acts on that fixed cell and determines the sideband <eigenvalues>. Translation invariance supplies zero <eigenfunctions> at $q=0$, namely spatial derivatives of the base pattern. Their small-$q$ <eigenvalues> determine long-wavelength <phase> stability; other parts of the spectrum can give independent instabilities.
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