Nonlinear Schrödinger Equation

Soliton Propagation & Collision
velocity₁
1.5
velocity₂
-1.5
amplitude₁
1.0
amplitude₂
1.0
nonlinearity g
1.0
|ψ|² density Re(ψ) Im(ψ)
i∂ψ/∂t = −½∂²ψ/∂x² − g|ψ|²ψ  (focusing NLS, g>0)
Bright solitons: ψ(x,t) = A·sech(A(x−vt))·e^{ivx−i(v²−A²)t/2}
Two solitons collide elastically, emerging unchanged in shape.