Korteweg–de Vries Equation
Cnoidal waves, solitons & nonlinear wave dispersion
Mode
Single Soliton
Cnoidal Wave
Soliton Collision
Parameters
Amplitude A:
1.0
Modulus m (cnoidal):
0.9
Speed c:
1.0
Dispersion β:
0.1
Equations
∂_t u + 6u∂_x u + ∂³_x u = 0
Soliton: u = A sech²(√(A/12) (x−ct))
Cnoidal: u = A cn²(κx; m)
Speed: c = 4κ²(1+m) (cnoidal)