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KdV Two-Soliton Collision — Finite-Difference Solver (2D)

Interactive 2D wave-height plot of the Korteweg-de Vries equation solved directly by finite differences (the Zabusky-Kruskal leapfrog scheme that first revealed solitons numerically in 1965) — watch a fast soliton overtake a slow one, with the exact Hirota closed-form solution and a live mass-conservation readout overlaid to verify the numerics in real time.

Mathematics2DAdvanced60 FPS📱 Mobile-adapted⇄ 3D version

This 2D companion to the 3D KdV soliton sim swaps the exact closed-form Hirota formula for a genuine numerical PDE solver: the same equation, u_t + 6uu_x + u_xxx = 0, is integrated forward step-by-step on a fixed grid using the Zabusky–Kruskal leapfrog finite-difference scheme — the historical method that first revealed solitons in 1965. Watch a fast, tall soliton overtake a slow, short one exactly as in the exact solution, while two independent live readouts — conservation of ∫u dx and the pointwise deviation from the exact Hirota reference — prove the raw numerics are actually converging to the right physics rather than merely animating a formula.

⚙ Under the hood

Watch the Korteweg-de Vries equation solved directly by finite differences (the 1965 Zabusky-Kruskal leapfrog scheme that first revealed solitons numerically) as a live 2D wave-height plot: a fast soliton overtakes a slow one, with the exact Hirota closed-form solution and a live mass-conservation readout overlaid to verify the raw numerics converge to the right physics in real time.

KdV equationSolitonsFinite differencesZabusky-Kruskal schemeMathematical physicsIntegrable systems

2D · HTML5 Canvas 2D · 60 FPS target · runs fully client-side, no install