Francois Belfort
May28-04, 05:46 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>\nAn acquaintance told me that all one needs\nto know about solitons is that they are a\nsingle travelling bumps, and that\nRussell discovered the relation between\nspeed v, amplitude A, and width lambda of a solitonic bump.\n\nHepretended (wrongly, I think) that this relation is given by\n\nv = 2A - 4/lambda^2\n\n(there is a dimensional problem)\nwhen the soliton local amplitude w is given as\n\nw(x,t)= A / cosh^2[(x-vt)/lambda]\n\nobeying the Korteweg-de Vries equation\n\n\\frac{\\partial w}{\\partial t} = \\frac{\\partial^3 w}{\\partial x^3}\n-6 w \\frac{\\partial w}{\\partial x}\n\n(which is also not ok in its dimensions) ?\n\nIt might be that I was given the wrong formula\nfor the speed-amplitude-width relation.\n\nCan somebody help out? My version of Mathematica is broken ...\n\nThanks for any help in advance!\n\nFB\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>An acquaintance told me that all one needs
to know about solitons is that they are a
single travelling bumps, and that
Russell discovered the relation between
speed v, amplitude A, and width \lambda of a solitonic bump.
Hepretended (wrongly, I think) that this relation is given by
v = 2A - 4/\lambda^2
(there is a dimensional problem)
when the soliton local amplitude w is given as
w(x,t)= A / cosh^2[(x-vt)/\lambda]
obeying the Korteweg-de Vries equation
\frac{\partial w}{\partial t} = \frac{\partial^3 w}{\partial x^3}-6 w \frac{\partial w}{\partial x}
(which is also not ok in its dimensions) ?
It might be that I was given the wrong formula
for the speed-amplitude-width relation.
Can somebody help out? My version of Mathematica is broken ...
Thanks for any help in advance!
FB
to know about solitons is that they are a
single travelling bumps, and that
Russell discovered the relation between
speed v, amplitude A, and width \lambda of a solitonic bump.
Hepretended (wrongly, I think) that this relation is given by
v = 2A - 4/\lambda^2
(there is a dimensional problem)
when the soliton local amplitude w is given as
w(x,t)= A / cosh^2[(x-vt)/\lambda]
obeying the Korteweg-de Vries equation
\frac{\partial w}{\partial t} = \frac{\partial^3 w}{\partial x^3}-6 w \frac{\partial w}{\partial x}
(which is also not ok in its dimensions) ?
It might be that I was given the wrong formula
for the speed-amplitude-width relation.
Can somebody help out? My version of Mathematica is broken ...
Thanks for any help in advance!
FB