OBSERVATION CONTRACT
Localized collision, not a wave show
The tau profile contains the cross coefficient q = ((k_fast - k_slow)/(k_fast + k_slow))^2. A linear sum cannot reproduce its collision shape or phase shift. The displayed speeds obey c = 2A.
OBSERVATION CHAMBER / ACTIVE
Soliton Scattering Field
Observe exact KdV single and two-soliton profiles: amplitude-speed coupling, collision phase shifts, conserved integrals, and a finite-difference PDE residual.
wave / nonlinear dispersion
Observation Model
ROUTE 79 / FIELD / WAVE / NONLINEAR DISPERSION
TAU PROFILE / PHASE SHIFT / CONSERVATION
When two localized waves pass through
Use the exact KdV tau profile to compare a single pulse with a two-soliton collision. The pulses keep their shape, exchange a measurable phase shift, and retain I1, I2, and H.
Canvas 2D + DOM fallback
The live ledger remains visible below when Canvas 2D is unavailable.
Focus the chart for Space/P PLAY, N STEP, R RESET, L lens, and arrow keys. Form inputs keep their native keyboard behavior.
TWO-SOLITON SCATTERING / PROFILE / t=0.00
- Time
- 0.00
- Fast amplitude A
- --
- Fast speed c=2A
- --
- Slow amplitude A
- --
- Slow speed c=2A
- --
- Phase shifts dx
- -- /
- --
- I1
- --
- I2
- --
- H
- --
- PDE residual
- --
- Finite
- YES
FIELD READOUT
Collision ledger
- Fast A / c
- --
- Slow A / c
- --
- Fast phase shift
- --
- Slow phase shift
- --
- I1 = integral u dx
- --
- I2 = integral u^2 dx
- --
- H = integral (u^3 - ux^2/2) dx
- --
- PDE residual
- --
- State
- finite / deterministic
DETERMINISTIC SELF-TEST
Tau acceptance
Fixed fixtures: k=.5 / kf=.8 / ks=.4 / exact tau / t=0
| CHECK | VALUE | LIMIT | RESULT |
|---|
Observation report
CONSERVATION LEDGER
I1, I2, H stay finite
For u = 2 d_xx log(tau), the field reports I1 = integral u dx, I2 = integral u^2 dx, and H = integral (u^3 - u_x^2/2) dx. Dashed bars show the exact multi-soliton references.
NUMERICAL CHECK
PDE residual and determinism
The residual is measured as R = u_t + 6u u_x + u_xxx with centered finite differences. The fixture repeats the same Float64 profile and checks finite values, speed, phase, invariants, and collision cross-term.
Formula note
tau = 1 + exp(2 eta_f) + exp(2 eta_s) + q exp(2 eta_f + 2 eta_s), eta_i = k_i (x - 4 k_i^2 t - x_i), and u = 2 d_xx log(tau). The phase shifts are dx_f = log((kf+ks)/(kf-ks))/kf and dx_s = -log((kf+ks)/(kf-ks))/ks.
OBSERVATION GUIDE
Touchpoints for observation
Start with TWO-SOLITON and PROFILE. Move TIME toward the collision, then use SCATTERING to compare base paths and shifts. Use INVARIANTS and RESIDUAL to inspect the numerical contract.
- Compare k_fast=.8, k_slow=.4 with the fixture values in the self-test.
- REPORT and PNG describe the current local screen. RESET removes old report and download state.
- Reduced motion keeps PLAY stopped. Visibility changes stop PLAY and do not advance hidden time.
This is a browser-side dimensionless KdV observation model. It does not claim a physical measurement, linear superposition, or a score.
Runs locally in the browser with no upload and no registration.
OBSERVATION POLICY
This field runs a deterministic dimensionless KdV tau profile in your browser. State, diagnostics, report, and PNG stay local. It does not measure visitors, devices, or physical matter.
Route
This chamber belongs to Fields in Motion.
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