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

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dc.creatorGrinevich, P. G.
dc.creatorKaipa, K. V.
dc.date2008-12-12
dc.date2009-04-23
dc.date.accessioned2026-07-07T13:07:06Z
dc.date.available2026-07-07T13:07:06Z
dc.descriptionThe 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 finite-gap solutions u(x,t) are expressed in terms of the Riemann theta-functions of a non-singular hyperelliptic curve $Γ$ and a positive generic divisor D of degree g on $Γ$, where the spectral data $(Γ, D)$ must satisfy some reality conditions. The problem addressed in note is: to calculate $\bar n$ directly from the theta-functional expressions for the solution u(x,t). The problem is solved here by introducing what we call the multiscale or elliptic limit of real finite-gap sine-Gordon solutions. We deform the spectral curve to a singular curve, for which the calculation of topological charges reduces to two special easier cases.
dc.identifierhttps://arxiv.org/abs/0812.2494
dc.identifierhttp://arxiv.org/abs/0812.2494
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227984
dc.subjectMathematical Physics
dc.titleCalculation of Topological Charge of Real Finite-Gap sine-Gordon solutions using Theta-functional formulae
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