Exact solutions of the focusing nonlinear Schrödinger equation i∂_t ψ + ½∂_xx ψ + |ψ|²ψ = 0. The Peregrine soliton reaches 3× the background amplitude — a mathematical model for rogue waves.
Solution Type
Max |ψ|: —
Background: —
NLS Breathers
Peregrine: rational, localized in x & t, max=3a
Akhmediev: periodic in x, localized in t (κ<√2 a)
Kuznetsov-Ma: localized in x, periodic in t (κ>√2 a)