NLS Bright Soliton
Bright soliton solutions of the nonlinear Schrödinger equation
Soliton 1
Amplitude A₁
1.0
Velocity v₁
0.5
Soliton 2
Amplitude A₂
1.5
Velocity v₂
-0.8
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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.