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
>
>

```

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