Re: kuen surface

*To*: mathgroup at smc.vnet.net*Subject*: [mg48044] Re: kuen surface*From*: "Roger L. Bagula" <rlbtftn at netscape.net>*Date*: Sat, 8 May 2004 01:23:50 -0400 (EDT)*References*: <c77982$hj3$1@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

You're looking for the "breather" equation associated with solitons. I'll copy the text part of my notebook ( there are actually a whole bunch of these surfaces: Clear[x,y,w,v,wb,nb,x1,y1,z1,p,q,c,d] (* My equations for pseudosphere matrix harmonic breathers*) (*cycloidal harmonics/ standing waves on the pseudosphere as Soliton breathers*) (* simpliar in structure to to the pin torus { Re[SphericalHarmonicY[3,3,t,p]],Im[SphericalHarmonicY[3,3,t,p]], SphericalHarmonicY[3,0,t,p]}*) (* by R. L. Bagula 27 May 2003©*) p=1 q=Sqrt[3] d=p/q c=Sqrt[1-d^2] (* with rotation matrix M *) M={{-Sin[t],-Cos[t],0},{Cos[t],-Sin[t],0},{0,0,1}} {x1,y1,z1}={0,0,x}-(2*d/c)* Cosh[c*x]/(c^2*Sin[d*t]^2+d^2*Cosh[c*x]^2)*( M.{Sin[d*t],d*Cos[d*t],d*Sinh[c*x]}) ga=ParametricPlot3D[{x1,y1,z1},{x,-3*Pi,3*Pi},{t,-3*Pi,3*Pi},PlotPoints->100, PlotRange->{{-3,3},{-3,3},{-5,5}},Boxed->False,Axes->False] Changing the ratio p/q gives a bunch of different surfaces: I think this specfic equation is due to Dr Sterling, but the breathers have been around in one form or another since Beltrami. Surfaces of constant negative curvature ( K= -1). bernazzani at mi.camcom.it wrote: > kindly I would want to know as the same graphics(kuen surface) is > constructed with Mathematica. > > I enclose the site from where I have taken the graphics > > http://math.cl.uh.edu/~gray/Gifccsurfs/ccsurfs.html > > > thanks > >