KdV Solitons — Nonlinear Wave Equation

Korteweg-de Vries equation: uₜ + 6uuₓ + uₓₓₓ = 0. Exact soliton solution: u = −(c/2) sech²[√(c/4)(x−ct)]. Higher-amplitude solitons travel faster. Two colliding solitons pass through each other unchanged — a hallmark of integrability.

Soliton 1 speed c₁3.0
Soliton 2 speed c₂1.2
Dispersion ε0.8
Speed multiplier4