NLS Bright Soliton

Bright soliton solutions of the nonlinear Schrödinger equation

Soliton 1

Soliton 2

Display

iψ_t + ½ψ_xx + |ψ|²ψ = 0

Bright soliton:
ψ = A·sech(A(x−vt))·exp(i(vx+(A²−v²/2)t))

Key property: two solitons pass through each other elastically — only a phase shift remains. Width ∝ 1/A, speed = v.