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Multiscale limit for finite-gap sine-Gordon solutions and calculation of topological charge using theta-functional formulae. (English. Russian original) Zbl 1181.35235
Proc. Steklov Inst. Math. 266, 49-58 (2009); translation from Tr. Mat. Inst. Steklova 266, 54-63 (2009).
Summary: We introduce the so-called multiscale limit for spectral curves associated with real finite-gap sine-Gordon solutions. This technique allows us to solve the old problem of calculating the density of the topological charge for real finite-gap sine-Gordon solutions directly from the \(\theta \)-functional formulae.
MSC:
35Q53 KdV equations (Korteweg-de Vries equations)
35C10 Series solutions to PDEs
35A16 Topological and monotonicity methods applied to PDEs
58J45 Hyperbolic equations on manifolds
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