Ridges on Breather surface

I needed to modify input for code somewhat through parameters $(text{ b ; lamb = CenAng }+pi)$ in order to specify a priori an integral number of Staves ( and the central polar angle CenAng ) for the Breather. This helped plot cusped longitudinal ridges and central stave mid-sections with any number of staves required.

In Prof. Palais' original there are approximately 22 ridges for constant $b=0.4,$ I took less number of staves 16 as under.

nStaves=6.;CenAng=2Pi/nStaves;lamb=Pi+CenAng;
b=Sqrt[CenAng(CenAng+2 Pi)]/(CenAng+Pi)
r=1-b^2;w=Sqrt[1-b^2];lamb=Pi/w;
    
Plot[(2 w/b)/Sqrt[(1-b^2 Cos[w v]^2)],{v,0,2lamb},GridLines->Automatic,PlotLabel->"MidSection Radii"]

deno[v_]=b*(w^2+(b*Sin[w*v])^2);
breather2D[v_]={2*w*(-(w*Sin[v]*Cos[w*v])+Cos[v]*Sin[w*v])/deno[v],2*w*(-(w*Cos[v]*Cos[w*v])-Sin[v]*Sin[w*v])/deno[v]};
    
ParametricPlot[breather2D[v],{v,-2lamb,8lamb},GridLines->Automatic,PlotStyle->{Thick,Blue},PlotLabel->" MidSection_PolarPlot_RIDGE_gourd"]
    con=2/b;x[u_]=con(Tanh[b u]-u/con);z[u_]=Sech[b u];
    
ParametricPlot[{z[u],x[u]},{u,-6,6},PlotPoints->60,GridLines->Automatic,PlotStyle->{Blue,Thick},PlotLabel->"RidgeLoop_Longitudinal",AspectRatio->1]
    denom[u_,v_]=b*((w*Cosh[b*u])^2+(b*Sin[w*v])^2);
    breather[u_,v_]={-u+(2*(1-b^2)*Cosh[b*u]*Sinh[b*u])/denom[u,v],(2*w*Cosh[b*u]*(-(w*Cos[v]*Cos[w*v])-Sin[v]*Sin[w*v]))/denom[u,v],(2*w*Cosh[b*u]*(-(w*Sin[v]*Cos[w*v])+Cos[v]*Sin[w*v]))/denom[u,v]};
    
ParametricPlot3D[breather[u,v],{u,-8,6},{v,-8 lamb,2 lamb},Mesh->Full,MaxRecursion->0,PlotPoints->{30,120},PlotStyle->{Thick,Yellow},PlotLabel->"BREATHER",Axes->False,Boxed->False]
    
ParametricPlot3D[breather[u,v],{u,-6,6},{v,8 lamb,10lamb},Mesh->Full,MaxRecursion->0,PlotPoints->{30,15},PlotStyle->{Yellow},PlotLabel->Two_Staves]

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