Solitons

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Solitons

• Historical information

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First observation of soliton by J.S.Russel

• In 1834, John Scott Russell describes his wave of
  translation. The discovery is described here in
  Russell's own words
• "I was observing the motion of a boat which was
  rapidly drawn along a narrow channel by a pair of
  horses, when the boat suddenly stopped - not so
  the mass of water in the channel which it had put
  in motion it accumulated round the prow of the
  vessel in a state of violent agitation, then
  suddenly leaving it behind, rolled forward with
  great velocity, assuming the form of a large
  solitary elevation, a rounded, smooth and
  well-defined heap of water, which continued its
  course along the channel apparently without
  change of form or diminution of speed. I followed
  it on horseback, and overtook it still rolling on
  at a rate of some eight or nine miles an hour,
  preserving its original figure some thirty feet
  long and a foot to a foot and a half in height.
  Its height gradually diminished, and after a
  chase of one or two miles I lost it in the
  windings of the channel. Such, in the month of
  August 1834, was my first chance interview with
  that singular and beautiful phenomenon which I
  have called the Wave of Translation".

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Explanation of Russels wave by Korteweg and de
Vries

• Russell's experimental work seemed at odds with
  the Isaac Newton and Daniel Bernoulli's theories
  of hydrodynamics. George Biddell Airy and George
  Gabriel Stokes had difficulty accepting Russell's
  experimental observations because they could not
  be explained by linear water wave theory. His
  contemporaries spent some time attempting to
  extend the theory but it would take until 1895
  before Diederik Korteweg and Gustav de Vries
  provided the theoretical explanation

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Resurrection of soliton

• All that time the scientists was not interested
  in solitons. It was the only particular fact. At
  that time the physical world seems to be linear.
• The resurrection of solitary wave was accidental.
  In 1952 Enrico Fermi asked D.Pasta and S.Ulam to
  conduct the numerical experiment to calculate
  the vibration of the link of 64 weights connected
  by nonlinear spring
• 
  Fk(?x)b(?x)2
• They observe that the system after some time
  returns to the initial state. They made this
  discovery when by chance let computer MANIAC run
  for long time.

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The KdV equation

• Latter the M.Kruskal and N.Zabuski had shown that
  such system is described by KdV equation.
• ut6 u ux-uxxx
• This equation has set of solutions with unique
  properties, which now we call solitons.
• The one-soliton solution

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• Three solitons solution
• Solitons can pass through each other without
  changing the form (like particles)

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Solitons nowadays

• Today solitons take apart in many physicals
  areas, like hydrodynamics, quantum mechanics,
  particle physics and so on.
• It was found a lots of equation with
  soliton-type solutions.

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A crazy idea from Tony Skyrme

• 1962 British scientist Tony Skyrme suggested a
  very interesting idea, namely can one create a
  fermion from a scalar field? The answer is YES
  and the result is skyrmion.
• A skyrmion is a homotopically non-trivial soliton
  solution of a nonlinear sigma model i.e., a
  particular case of a topological soliton.
• If spacetime has the topology S3R (for space and
  time respectively), then classical configurations
  are classified by an integral winding number
  because the third homotopy group
  p3(SU(N)xSU(N)/SU(N))Z

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Baryon Rotierendes Soliton

• Soliton Kollektive Rotation um 8 Achsen im
  Spin-Flavour-Raum
• Wess-Zumino-Term schränkt Rotation ein ? 8, 10,
  10, 27, ..
• Wess-Zumino-Term berücksichtigt axiale Anomalie
  der QCD

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Pentaquark
The antiquark has a different flavor than the
other 4 quarks.
D. Diakonov, V. Petrov, and M. Polyakov, Z. Phys.
A 359 (1997) 305.

• Exotic S1
• Low mass 1530 MeV
• Narrow width 15 MeV
• Jp1/2

M 1890-180Y MeV
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Soliton wave
From Memory Alpha, the free Star Trek reference
A report from year 2368 ? http//memory-alpha.org
/de/wiki/Die_Soliton-Welle

A soliton wave.
A soliton wave is a confined energy phenomenon
that travels at faster-than-light speeds, with
potential applications in spacecraft propulsion.
In the 24th century, Doctor Ja'Dar of Bilana III
investigated soliton waves as a possible
alternative to warp drive. The USS Enterprise-D
attended the first field test of this technology
in 2368. The test involved the generation of a
soliton wave using 23 field coils on the surface
of Bilana III, which would envelop a small,
unmanned vehicle and push it into warp towards
Lemma II. There, a sister facility would generate
a scattering field to dissipate the wave and
bring the test ship out of warp. Although the
test began promisingly, displaying a 98 energy
transfer efficiency of the soliton wave that was
450 more efficient than the Enterprise's own
warp engines, the wave unexpectedly destabilized
and manifested a subspace distortion that
destroyed the test ship and damaged the
Enterprise. Dr. Ja'Dar believed that a transient
power imbalance was responsible. The Enterprise
subsequently found that the wave was accelerating
towards Lemma II, gaining energy in the process.
It was estimated that by the time the wave
arrived it would contain enough energy to destroy
most of the planet. The wave had grown too
powerful for the Lemma II facility to dissipate,
but the Enterprise was able to disrupt the wave
by detonating five photon torpedoes directly in
front of it. (TNG "New Ground")