Stability Criterion for Dark Solitons

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Abstract
We prove that the inequality ∂P/∂v<0 is the stability criterion for dark solitons of the one-dimensional nonlinear Schrödinger equation with general nonlinearity. Here v is the soliton's velocity, and P renormalized momentum: P=(i/2)∫(ψx*ψ−ψxψ*)(1−ρ0/|ψ|2)dx.

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