KdV Solitons (Exact)

This interactive simulator explores KdV Solitons (Exact) in Waves & Sound. u_t + 6uu_x + u_xxx = 0; Hirota two-soliton collision or one sech² pulse. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Waves & Sound.

Key terms

  • kdv
  • solitons
  • exact
  • kdv soliton
  • waves
  • sound

How it works

**Korteweg–de Vries** equation in the standard form **u_t + 6u u_x + u_xxx = 0**. The **two-hump** curve is the **exact Hirota** solution: taller, faster solitons overtake shorter ones and emerge with nearly the same shapes — the classic **nonlinear superposition** demo.

Key equations

u = 2 ∂²_xx ln τ, τ = 1 + exp(θ₁) + exp(θ₂) + A exp(θ₁+θ₂), θⱼ = kⱼx − 4kⱼ³t
One soliton: u = 2k² sech²(k(x − x₀ − 4k²t))