Topological charges and the genus of surfaces

[摘要] We show that the topological charge of the n-soliton solution of the sine-Gordon equation n[phi] = (1/2 pi)[integral dx partial derivative(x) phi] is related to the genus g > 1 of a constant negative curvature compact orientable surface described by this configuration. The relation is n = 2(g - 1), where n = 2 nu is even. The moduli space of complex dimension B-g = 3(g - 1) corresponds precisely to the freedom to choose the configuration with n solitons of arbitrary positions and velocities. We speculate also that the odd soliton states will described the unoriented surfaces.

[发布日期] 1997-08-01

[关键词] solitons;Sine-Gordon equation;topological charges;(Riemann) surfaces;moduli spaces