Peregrine Soliton & Modulation Instability

Modulation Instability & Peregrine

NLS equation: iψ_t + ½ψ_xx + |ψ|²ψ = 0. Modulation instability creates "rogue waves". The Peregrine soliton: rational solution localized in both x and t.

|ψ_P| = |1 - 4(1+2it)/(1+4x²+4t²)|

Mode number k: 1 Perturbation ε: 0.10 Time speed: 1.0