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===Mathematical derivation of gain spectrum===
The gain spectrum can be derived <ref name="agrawal" /> by starting with a model of modulation instability based upon the [[nonlinear Schrödinger equation]]{{what|reason=Time and space reversed?}}
: <math>\frac{\partial A}{\partial z} + i\beta_2\frac{\partial^2A}{\partial t^2} = i\gamma|A|^2A,</math>
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