Soliton Collision

Nonlinear self-reinforcing solitary wave packets governed by the KdV equation, colliding and emerging unchanged in shape.

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60 FPS • Canvas 2D

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Live Parameters

Pulse Amplitude 45

Peak soliton height

Propagation Velocity 1

Non-linear wave speed

Mathematical Formulation

68 chars medium

Analytical Equation

\frac{\partial u}{\partial t} + 6u \frac{\partial u}{\partial x} + \frac{\partial^3 u}{\partial x^3} = 0, \quad u(x,t) = 2k^2 \operatorname{sech}^2(k(x - 4k^2 t))

Compact Formula

u(x, t) = 2k² * sech²(k(x - 4k² t)), total_u = u1(x, t) + u2(x, -t)

Renderer Logic

const pos1 = k1 * (normX - 4 * k1 * k1 * (t * 0.8 - 4) + phaseShift);
const sech1 = 1 / Math.cosh(pos1);
const u1 = 2 * k1 * k1 * sech1 * sech1;

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#soliton #kdv #non-linear #hydrodynamics #waves #physics

Author: Math Art Core Target: 60 FPS

Soliton Collision

Live Parameters

Mathematical Formulation

Mathematical Tags

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