Focusing nonlinear Schrodinger modulation dispersion
= Focusing nonlinear Schrodinger modulation dispersion
{title2=$\Omega^2=\chi K^2(\chi K^2-2\mu)$}
For $-iA_t+\chi A_{xx}-\mu A+\delta A|A|^2=0$ with positive coefficients, linearize around $A=\sqrt{\mu/\delta}$ using real amplitude and phase perturbations. Their two-by-two <dispersion relation> gives the displayed equation. The <modulational instability> band is $0<K^2<2\mu/\chi$, with maximum <growth rate> $\mu$ at $K^2=\mu/\chi$.