Two-Soliton Surface

2soliton symKuen morph 001
In the 2-parameter family of 2-soliton surfaces lies this symmetric deformation of the Kuen Surface

The Two-Soliton Surface surface is the surface of Gaussian curvature K = -1 that corresponds to the following solution of the Sine-Gordon equation:

q(u,v) := 4 * arctan( B * (exp(A2(u, v)) - exp(A1(u, v))) / (1 + exp(A1(u, v) + A2(u, v))));

where:

B := (cos(bb * pi) - cos(aa * pi)) / (cos((bb - aa) * pi) - 1);

A1 := cosec(aa * pi) * u - cotan(aa * pi) * v;

A2 := cosec(bb * pi) * u - cotan(bb * pi) * v;
2 soliton leave symmetr 001
2-soliton surface with varying parameter, starting from the Kuen Surface.
2 soliton equal params 001
The soliton solution formula gives 0/0 when the two parameters are equal, but a limit exists. This animation is close to the limit 1-parameter solution.
two soliton st
two soliton st
two soliton sw
two soliton sw

Related Surface

  1. Dini Surface
  2. Breather Surface
  3. Kuen Surface
  4. Two-Soliton Surface
  5. Three-Soliton

SGE_SolitonSurfaces.pdf