Calculation of Topological Charge of Real Finite-Gap sine-Gordon solutions using Theta-functional formulae

P. G. Grinevich, K. V. Kaipa

The most basic characteristic of x-quasiperiodic solutions u(x,t) of the sine-Gordon equation u_{tt}-u_{xx}+\sin u=0 is the topological charge density denoted $\bar{n}$. The real fi…