= Fibre modulational instability
{title2=$K^2=(\beta_2\Omega^2/2)(\beta_2\Omega^2/2+2\gamma P)$}
Linearizing a uniform Kerr-fibre background couples opposite <frequency> sidebands. With $iA_z-\beta_2A_{TT}/2+\gamma|A|^2A=0$, the displayed <dispersion relation> permits exponential growth precisely when $\beta_2\gamma<0$ and $0<\Omega^2<-4\gamma P/\beta_2$. For positive $\gamma$, this is anomalous <group velocity dispersion>. <complex conjugation> requires the paired complex-mode ansatz on the unstable branch. <amplitude> and <power> growth exponents differ by a factor of two.
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