soliton.mht

华中科技大学光电子科学与工程学院本科光纤通信课程教学课件（双语教学）

      of the field equations. The constraint arises almost always =
because the=20
      differential equations must obey a set of <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/boundary+conditions">bo=
undary=20
      conditions</A>, and the boundary has a non-trivial <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/homotopy+group">homotop=
y=20
      group</A>, preserved by the differential equations. Thus, the =
solutions of=20
      the differential equations can be classified into <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/homotopy+class">homotop=
y=20
      classes</A>. There is no continuous transformation that will map a =

      solution in one homotopy class to another; thus the solutions are =
truly=20
      distinct, and maintain their integrity, even in the face of =
extremely=20
      powerful forces. Examples of topological solitons include the =
screw=20
      dislocation in a <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/crystalline+lattice">cr=
ystalline=20
      lattice</A>, the <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Dirac+string">Dirac=20
      string</A> and the <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/magnetic+monopole">magn=
etic=20
      monopole</A> in <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/electromagnetism">elect=
romagnetism</A>,=20
      the <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Skyrmion">Skyrmion</A> =
and=20
      the <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Wess-Zumino-Witten+mode=
l">Wess-Zumino-Witten=20
      model</A> in <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/quantum+field+theory">q=
uantum=20
      field theory</A>, and <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/cosmic+string">cosmic=20
      strings</A> and <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/domain+wall">domain=20
      walls</A> in <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/physical+cosmology">cos=
mology</A>.=20

      <H2>History</H2>In 1834, <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/John+Scott+Russell">Joh=
n=20
      Scott Russell</A> describes his <EM>wave of translation</EM>. =
<BR><BR>In=20
      1965 Norman Zabusky of <A=20
      href=3D"http://encyclopedia.thefreedictionary.com/Bell+Labs">Bell =
Labs</A>=20
      and <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Martin+Kruskal">Martin =

      Kruskal</A> of <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Princeton+University">P=
rinceton=20
      University</A> first demonstrated soliton behaviour in media =
subject to=20
      the Korteweg-de Vries equation (KdV equation) in a computational=20
      investigation using a <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/finite+difference">fini=
te=20
      difference</A> approach. <BR><BR>In 1967, Gardner, Greene, Kruskal =
and=20
      Miura discovered an <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/inverse+scattering+tran=
sform">inverse=20
      scattering transform</A> enabling <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/analytic+function">anal=
ytical</A>=20
      solution of the KdV equation. The work of <A=20
      href=3D"http://encyclopedia.thefreedictionary.com/Peter+Lax">Peter =
Lax</A>=20
      on <A =
href=3D"http://encyclopedia.thefreedictionary.com/Lax+pair">Lax=20
      pairs</A> and the Lax equation has since extended this to solution =
of many=20
      related soliton-generating systems.=20
      <H2>Solitons in fiber optics</H2>In 1973, Akira Hasegawa of <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/AT%26T">AT&amp;T</A> =
<A=20
      href=3D"http://encyclopedia.thefreedictionary.com/Bell+Labs">Bell =
Labs</A>=20
      was the first to suggest that solitons could exist in <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/optical+fiber">optical =

      fibers</A>, due to a balance between <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/self-phase+modulation">=
self-phase=20
      modulation</A> and <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/dispersion+(optics)">an=
omalous=20
      dispersion</A>. He also proposed the idea of a soliton-based =
transmission=20
      system to increase performance of optical <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/telecommunications">tel=
ecommunications</A>.=20
      <BR><BR>Solitons in a fiber optic system are described by the <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Manakov+equations">Mana=
kov=20
      equations</A>. <BR><BR>In 1987, P. Emplit, J.P. Hamaide, F. =
Reynaud, C.=20
      Froehly and A. Barthelemy, from the Universities of Brussels and =
Limoges,=20
      made the first experimental observation of the propagation of a =
dark=20
      soliton, in an optical fiber. <BR><BR>In 1988, Linn Mollenauer and =
his=20
      team transmitted soliton pulses over 4,000 kilometers using a =
phenomenon=20
      called the <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Raman+effect">Raman=20
      effect</A>, named for the Indian scientist <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Chandrasekhara+Venkata+=
Raman">Sir=20
      C. V. Raman</A> who first described it in the <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/1920s">1920s</A>, to=20
      provide optical gain in the fiber. <BR><BR>In 1991, a Bell Labs =
research=20
      team transmitted solitons error-free at 2.5 gigabits per second =
over more=20
      than 14,000 kilometers, using <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/erbium">erbium</A> =
optical=20
      fiber amplifiers (spliced-in segments of optical fiber containing =
the rare=20
      earth element erbium). Pump lasers, coupled to the optical =
amplifiers,=20
      activate the erbium, which energizes the light pulses. <BR><BR>In =
1998,=20
      Thierry Georges and his team at <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/France+T%E9l%E9com">Fra=
nce=20
      T=C3=A9l=C3=A9com</A> R&amp;D Center, combining optical solitons =
of different=20
      wavelengths (<A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/wavelength+division+mul=
tiplexing">wavelength=20
      division multiplexing</A>), demonstrated a data transmission of 1 =
<A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/Binary+prefix">terabit<=
/A>=20
      per second (1,000,000,000,000 units of information per second). =
<BR><BR>In=20
      2001, the practical use of solitons became a reality when Algety =
Telecom=20
      deployed submarine <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/telecommunications">tel=
ecommunications</A>=20
      equipment in Europe carrying real traffic using <A=20
      =
href=3D"http://encyclopedia.thefreedictionary.com/John+Scott+Russell">Joh=
n=20
      Scott Russell</A>'s solitary wave. (Note by a reader in 2007: =
Algety may=20
      have gone bust. The present status of using optical soliton for=20
      communication is not clear and more information is needed.) =
<BR><BR>For=20
      some reasons, it is possible to observe both positive and negative =

      solitons in optic fibre. However, usually only positive solitons =
are=20
      observed for water wave.=20
      <H2>Bions</H2>
      <DIV class=3D"messagebox cleanup metadata plainlinks">
      <TABLE=20
      style=3D"BACKGROUND: none transparent scroll repeat 0% 0%; WIDTH: =
99%">
        <TBODY>
        <TR>
          <TD><B>Please help [ improve this article] by expanding this=20
            section.</B><BR><SMALL>See talk page for details. Please =
remove this=20
            message once the section has been expanded. (tagged since =
<B>April=20
            2007</B>)</SMALL></TD></TR></TBODY></TABLE></DIV><BR><BR>The =
bound state=20
      of two solitons is known as a <EM>bion</EM>.=20
      <H2>See also</H2>
      <UL>
        <LI><A=20
        =
href=3D"http://encyclopedia.thefreedictionary.com/Soliton+(topological)">=
Soliton=20
        (topological)</A>.=20
        <LI><A=20
        =
href=3D"http://encyclopedia.thefreedictionary.com/Solitary+wave">Solitary=
=20
        waves</A> in discrete media <A=20
        =
href=3D"http://www.livescience.com/technology/050614_baby_waves.html"=20
        =
target=3D_blank>http://www.livescience.com/technology/050614_baby_waves.h=
tml</A>=20

        <LI><A =
href=3D"http://encyclopedia.thefreedictionary.com/Freak+wave">Freak=20
        waves</A> may be a related phenomenon.=20
        <LI><A=20
        =
href=3D"http://encyclopedia.thefreedictionary.com/Topological+quantum+num=
ber">Topological=20
        quantum number</A>=20
        <LI><A=20
        =
href=3D"http://encyclopedia.thefreedictionary.com/Oscillon">Oscillons</A>=
=20
        <LI><A=20
        =
href=3D"http://encyclopedia.thefreedictionary.com/Soliton+model">Soliton =

        model</A> of nerve impulse propagation </LI></UL>
      <H2>References</H2>
      <UL>
        <LI>N. J. Zabusky and M. D. Kruskal (1965). <EM>Interaction of=20
        'Solitons' in a Collisionless Plasma and the Recurrence of =
Initial=20
        States.</EM> Phys Rev Lett 15, 240=20
        <LI>A. Hasegawa and F. Tappert (1973). <EM>Transmission of =
stationary=20
        nonlinear optical pulses in dispersive dielectric fibers. I. =
Anomalous=20
        dispersion.</EM> Appl. Phys. Lett. Volume 23, Issue 3, pp. =
142-144.=20
        <LI>P. Emplit, J.P. Hamaide, F. Reynaud, C. Froehly and A. =
Barthelemy=20
        (1987) <EM>Picosecond steps and dark pulses through nonlinear =
single=20
        mode fibers.</EM> Optics. Comm. 62, 374=20
        <LI>P. G. Drazin and R. S. Johnson (1989). <EM>Solitons: an=20
        introduction.</EM> Cambridge University Press. </LI></UL>
      <H2>External links</H2>
      <UL>
        <LI><A href=3D"http://www.morningglorycloud.com/"=20
        target=3D_blank>morningglorycloud.com</A> has video of the =
Morning Glory=20
        Cloud in Australia's Gulf of Carpentaria=20
        <LI><A=20
        =
href=3D"http://www.sciencedaily.com/releases/2005/05/050506141331.htm"=20
        target=3D_blank>Solitons, solitary waves and secondary or baby =
solitary=20
        waves in discrete media</A>=20
        <LI><A href=3D"http://www.ma.hw.ac.uk/solitons/" =
target=3D_blank>Heriot-Watt=20
        University soliton page</A>=20
        <LI><A=20
        =
href=3D"http://www.math.h.kyoto-u.ac.jp/~takasaki/soliton-lab/gallery/sol=
itons/index-e.html"=20
        target=3D_blank>The many faces of solitons</A>=20
        <LI><A =
href=3D"http://www.usf.uni-osnabrueck.de/~kbrauer/solitons.html"=20
        target=3D_blank>Klaus Brauer's soliton page</A>=20
        <LI><A =
href=3D"http://homepages.tversu.ru/~s000154/collision/main.html"=20
        target=3D_blank>Solitons and Soliton Collisions</A>=20
        <LI><A href=3D"http://www.ma.hw.ac.uk/~chris/scott_russell.html" =

        target=3D_blank>John Scott Russell and the solitary wave</A>=20
        <LI><A href=3D"http://www.severn-bore.co.uk/default.htm"=20
        target=3D_blank>Severn Bore web site</A>=20
        <LI><A =
href=3D"http://www.ma.hw.ac.uk/solitons/LocalHeroes/sr.html"=20
        target=3D_blank>John Scott Russell biography</A>=20
        <LI><A href=3D"http://www.its.caltech.edu/~ehsan" =
target=3D_blank>Soliton in=20
        Electrical Engineering</A>=20
        <LI><A href=3D"http://web.njit.edu/~miura/" =
target=3D_blank>Miura's home=20
        page</A>=20
        <LI><A href=3D"http://www.ma.hw.ac.uk/solitons/soliton1b.html"=20
        target=3D_blank>Photograph of Soliton on the Scott Russell =
Aqueduct</A>=20
        <LI><A href=3D"http://www.pnas.org/cgi/reprint/102/28/9790"=20
        target=3D_blank>Solitons possible agent of nerve transmission=20
        (PDF)(pnas.org)</A> </LI></UL>
      <DIV class=3Dhint id=3DTp1><B>Mathematics</B> (colloquially, =
<B>maths</B> or=20
      <B>math</B>) is the body of knowledge centered on such concepts as =

      quantity, structure, space, and change, and also the academic =
discipline=20
      that studies them. Benjamin Peirce called it "the science that =
draws=20
      necessary conclusions".<BR><B>.....</B> <SPAN class=3Dflw>Click =
the link for=20
      more information.</SPAN> </DIV>
      <DIV class=3Dhint id=3DTp2><B>Physics</B> is the science of=20
      <EM>matter</EM><SUP>[1]</SUP> <EM>and its=20
      motion</EM><SUP>[2]</SUP><SUP>[3]</SUP>, as well as <EM>space and=20
      time</EM><SUP>[4]</SUP><SUP>[5]</SUP> =E2=80=94the science that =
deals with=20
      concepts such as force, energy, mass, and charge.<BR><B>.....</B> =
<SPAN=20
      class=3Dflw>Click the link for more information.</SPAN> </DIV>
      <DIV class=3Dhint id=3DTp3><B>nonlinear system</B> is a system =
which is not=20
      linear i.e. a system which does not satisfy the superposition =
principle.=20
      Less technically, a nonlinear system is any problem where the =
variable(s)=20
      to be solved for cannot be written as a linear sum of independent=20
      components.<BR><B>.....</B> <SPAN class=3Dflw>Click the link for =
more=20
      information.</SPAN> </DIV>
      <DIV class=3Dhint id=3DTp4>In mathematics, a <B>partial =
differential=20
      equation</B> (<B>PDE</B>) is a type of differential equation, i. =
e. a=20
      relation involving an unknown function of several independent =
variables=20
      and its partial derivatives with respect to those=20
      variables.<BR><B>.....</B> <SPAN class=3Dflw>Click the link for =
more=20
      information.</SPAN> </DIV>
      <DIV class=3Dhint id=3DTp5><B>John Scott Russell</B> (9 May 1808, =
Glasgow =E2=80=93 8=20
      June 1882) was a Scottish naval engineer who built the <EM>Great=20
      Eastern</EM> (the largest ship built at that time) in =
collaboration with=20
      Isambard Kingdom Brunel, and made the discovery that gave birth to =
the=20
      modern study of<BR><B>.....</B> <SPAN class=3Dflw>Click the link =
for more=20