soliton equations Text - Physics Forums Library

Mayer Humi

Jul12-04, 04:44 AM

tessel@tum.bot

Jul13-04, 03:37 AM

<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Mon, 12 Jul 2004, Mayer Humi wrote:\n\n> I am wondering if somebody can point out readable references\n> that derive the Kdv and other soliton eqs from (generic) physical\n> systems e.g. "deep water waves" etc.\n\nFor KdV, try\n\nauthor = {Horace Lamb},\ntitle = {Hydrodynamics},\nnote = {reprint of sixth edition, 1932; first edition 1879}\npublisher = {Dover},\nyear = 1945}\n\nMore generally, you can try the first article in the collection\n\neditor = {Gu Chaohao},\ntitle = {Soliton Theory and Its Applications},\npublisher = {Springer-Verlag},\nyear = 1990}\n\nA very important skill is learning how to extract left and right moving\nKdV from Boussinesq. For this (and lots lots more), see either of\n\nauthor = {Richard S. Palais},\ntitle = {The Symmetries of Solitons},\njournal = {Bull. of the A. M. S.}\nvolume = {?},\nyear = {1997}\nnote = {dg-ga/9708004}}\n\neditor = {A. P. Fordy and J. C. Wood},\ntitle = {Harmonic Maps and Integrable Systems},\nseries = {Aspects of Mathematics},\nvolume = {E23},\npublisher = {Vieweg},\nyear = 1994,\nnote = {available at\nhttp://www.amsta.leeds.ac.uk/Pure/staff/wood/FordyWood/contents.html}}\n\nNotice these are available on-line and I have found them to be superb.\n\nYou can also see the references in Palais or Fordy & Wood. For example,\nto read more about the vortex filaments I mentioned and how their\nevolution reduces to "move in the direction of the binormal with speed\nproportional to the torsion". I should have said, "c.f. evolution by\ncurvature minimization as in Thurston program and other famous ideas"---\nthis kind of evolution defined in vivid geometric terms has a long and\nvaried history in its own right.\n\n"T. Essel" (hiding somewhere in cyberspace)\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form">  View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Mon, 12 Jul 2004, Mayer Humi wrote:

> I am wondering if somebody can point out readable references
> that derive the Kdv and other soliton eqs from (generic) physical
> systems e.g. "deep water waves" etc.

For KdV, try

author = {Horace Lamb},
title = {Hydrodynamics},
note = {reprint of sixth edition, 1932; first edition 1879}
publisher = {Dover},
year = 1945}

More generally, you can try the first article in the collection

editor = {Gu Chaohao},
title = {Soliton Theory and Its Applications},
publisher = {Springer-Verlag},
year = 1990}

A very important skill is learning how to extract left and right moving
KdV from Boussinesq. For this (and lots lots more), see either of

author = {Richard S. Palais},
title = {The Symmetries of Solitons},
journal = {Bull. of the A. M. S.}
volume = {?},
year = {1997}
note = {dg-ga/9708004}}

editor = {A. P. Fordy and J. C. Wood},
title = {Harmonic Maps and Integrable Systems},
series = {Aspects of Mathematics},
volume = {E23},
publisher = {Vieweg},
year = 1994,
note = {available at
http://www.amsta.leeds.ac.uk/Pure/staff/wood/FordyWood/contents.html}}

Notice these are available on-line and I have found them to be superb.

You can also see the references in Palais or Fordy & Wood. For example,
to read more about the vortex filaments I mentioned and how their
evolution reduces to "move in the direction of the binormal with speed
proportional to the torsion". I should have said, "c.f. evolution by
curvature minimization as in Thurston program and other famous ideas"---
this kind of evolution defined in vivid geometric terms has a long and
varied history in its own right.

"T. Essel" (hiding somewhere in cyberspace)