Soliton Collision

Korteweg–de Vries Equation: u_t + 6uu_x + u_xxx = 0
4.0
1.0
2.0
0.8
KdV solitons are exact solitary wave solutions that pass through each other unchanged — only a phase shift remains after collision. Taller solitons travel faster (speed ∝ amplitude²). This elastic interaction is a hallmark of integrability. The two-soliton solution is given by the Hirota bilinear method.