• Black Soliton physics hoodie, pixel-art KdV soliton collision design, worn by a model, front close-up
  • Black Soliton physics hoodie, pixel-art KdV soliton collision design, worn by a model, back close-up
  • Black Soliton physics hoodie, pixel-art KdV soliton collision design, front view
  • Black Soliton physics hoodie, pixel-art KdV soliton collision design, back view
  • Black Soliton physics hoodie, pixel-art KdV soliton collision design, turning on a model
  • Black Soliton physics hoodie, ΨP Pixelated Physics neck label
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Soliton HoodieTHEY PASS THROUGH UNHARMED | Pixelated Physics

Soliton Hoodie – THEY PASS THROUGH UNHARMED | Pixelated Physics

$54.99 USD
$54.99 USD
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Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Color
Black
Size
S–5XL
Made
To order · shipping times

In 1834 John Scott Russell followed a single hump of water on horseback along a Scottish canal for more than a mile. It did not spread out. The exact two-soliton solution of the KdV equation in space and time: the tall fast wave overtakes the short one; both survive. Pixel-art unisex hoodie in black; equation, symbols and sources in the physics panel below.

Color
Size

Size guideS–5XL · inches

Details

Size & fitS–5XL

Unisex Heavy Blend hoodie (Gildan 18500), classic fit.

SizeWidthLengthSleeve
S202733.5
M222834.5
L242935.5
XL263036.5
2XL283137.5
3XL303238.5
4XL323339.5
5XL343440.5

Measurements in inches. Width and length ±1 in, sleeve (from center back) ±0.75 in.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

In 1834 John Scott Russell followed a single hump of water on horseback along a Scottish canal for more than a mile. It did not spread out.

Normally waves disperse. In shallow water a nonlinear steepening effect can balance that dispersion exactly, and the Korteweg–de Vries equation of 1895 describes it. Its lone-wave solutions travel at a speed that grows with their height.

The art is the exact two-soliton solution, written out by Ryogo Hirota in 1971, with position across and time up. The taller, faster wave catches the shorter one, they merge, and they come out unchanged except for a small jump in position.

Zabusky and Kruskal coined the word soliton in 1965 because the waves collide like particles.

They pass through unharmed.

Equations

\[u_t + 6uu_x + u_{xxx} = 0\]
\[u = 2\,\partial_x^2\ln F\]
\[F = 1 + e^{\eta_1} + e^{\eta_2} + A\,e^{\eta_1+\eta_2},\quad \eta_i = k_ix - k_i^3t + \delta_i,\quad A = \left(\frac{k_1-k_2}{k_1+k_2}\right)^2\]
SymbolMeaningUnit
\(u\) wave height (scaled) \(\mathrm{1}\)
\(x, t\) position and time (scaled) \(\mathrm{1}\)
\(k_1, k_2\) soliton wavenumbers; amplitude k^2/2, speed k^2 \(\mathrm{1}\)
\(\eta_i\) phase of soliton i \(\mathrm{1}\)
\(\delta_i\) initial offset \(\mathrm{1}\)
\(A\) interaction coefficient \(\mathrm{1}\)
\(F\) Hirota tau function \(\mathrm{1}\)

Sources

  1. Russell (1845) Report on Waves, Report of the 14th Meeting of the British Association for the Advancement of Science, 311
  2. Korteweg & de Vries (1895) On the change of form of long waves advancing in a rectangular canal, Phil. Mag. 39, 422
  3. Zabusky & Kruskal (1965) Interaction of Solitons in a Collisionless Plasma, Phys. Rev. Lett. 15, 240
  4. Hirota (1971) Exact Solution of the Korteweg–de Vries Equation for Multiple Collisions of Solitons, Phys. Rev. Lett. 27, 1192
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