KdV Soliton Collision

Nonlinear Wave Dynamics — Two-Soliton Exact Solution
Amplitude 1 (c₁)2.0
Amplitude 2 (c₂)0.5
Speed1.0
Phase shift δ:— Soliton 1 speed:— Soliton 2 speed:—
The KdV equation u_t + 6u·u_x + u_xxx = 0 admits exact N-soliton solutions via inverse scattering. Two solitons collide and emerge intact — only a phase shift remains: δ = log|(c₁+c₂)/(c₁−c₂)|. Solitons exist due to perfect balance between nonlinear steepening and dispersive spreading.