m at h . D G ] 2 8 Fe b 20 05 Initial Value Problems of the Sine - Gordon Equation and Geometric Solutions
نویسنده
چکیده
Recent results using inverse scattering techniques interpret every solution φ(x, y) of the sine-Gordon equation as a non-linear superposition of solutions along the axes x = 0 and y = 0. This has a well-known geometric interpretation, namely that every weakly regular surface of Gauss curvature K = −1, in arc length asymptotic line parametrization, is uniquely determined by the values φ(x, 0) and φ(0, y) of its coordinate angle along the axes. We introduce a generalized Weierstrass representation of pseudospherical surfaces that depends only on these values, and we explicitely construct the associated family of pseudospherical immersions corresponding to it. Mathematics Subject Classification: 53A10, 58E20
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