Benjamin-Feir (1967): a uniform
wave train is unstable to
amplitude modulations when
k₀ > 1/√2 (deep water).

Growth rate: σ = q√(k₀²A²-q²/4)
Unstable when: q < 2k₀A

NLS eq: i∂ψ/∂t + ∂²ψ/∂x² + 2|ψ|²ψ=0
Leads to Akhmediev breathers.