KdV Soliton Collision — Elastic Scattering
Two-soliton exact solution: emerge from collision unchanged except for phase shift
t = 0.00
The Korteweg-de Vries equation u_t + 6uu_x + u_xxx = 0 admits exact N-soliton solutions
via the inverse scattering transform (Gardner-Greene-Kruskal-Miura 1967).
Two solitons collide and emerge perfectly intact — amplitude and shape preserved.
The only trace is a phase shift: each soliton is displaced from where it would have been
without collision. Faster soliton is taller (speed ∝ amplitude²/3) and shifts forward;
slower shifts backward. The exact 2-soliton formula is plotted analytically.