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 Zap. Nauchn. Sem. LOMI, 1984, Volume 133, Pages 177–196 (Mi znsl4418)

Algebro-topological approach to reality problems. Real action variables in the theory of finite-gap solutions of the Sine-Gordon equations

S. P. Novikov

Abstract: The paper developes an algebro-topological approach to the problem of effective selection of real finite gap solutions of the sine-Gordon equation, based on the so-called $\gamma$-representation associated with a Riemann surface where action variables can be written in a closed form. The approach is a general one and applies to many other systems for which the reality problem has not yet been solved.

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Bibliographic databases:
UDC: 519.4

Citation: S. P. Novikov, “Algebro-topological approach to reality problems. Real action variables in the theory of finite-gap solutions of the Sine-Gordon equations”, Differential geometry, Lie groups and mechanics. Part VI, Zap. Nauchn. Sem. LOMI, 133, "Nauka", Leningrad. Otdel., Leningrad, 1984, 177–196

Citation in format AMSBIB
\Bibitem{Nov84} \by S.~P.~Novikov \paper Algebro-topological approach to reality problems. Real action variables in the theory of finite-gap solutions of the Sine-Gordon equations \inbook Differential geometry, Lie groups and mechanics. Part~VI \serial Zap. Nauchn. Sem. LOMI \yr 1984 \vol 133 \pages 177--196 \publ "Nauka", Leningrad. Otdel. \publaddr Leningrad \mathnet{http://mi.mathnet.ru/znsl4418} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=742157} \zmath{https://zbmath.org/?q=an:0546.35071} 

• http://mi.mathnet.ru/eng/znsl4418
• http://mi.mathnet.ru/eng/znsl/v133/p177

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. E. D. Belokolos, A. I. Bobenko, V. B. Matveev, V. Z. Ènol'skii, “Algebraic-geometric principles of superposition of finite-zone solutions of integrable non-linear equations”, Russian Math. Surveys, 41:2 (1986), 1–49
2. B. A. Dubrovin, S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamiltonian theory”, Russian Math. Surveys, 44:6 (1989), 35–124
3. P. G. Grinevich, S. P. Novikov, “Real finite-zone solutions of the sine-Gordon equation: a formula for the topological charge”, Russian Math. Surveys, 56:5 (2001), 980–981
4. Yu. V. Brezhnev, “Finite-Band Potentials with Trigonal Curves”, Theoret. and Math. Phys., 133:3 (2002), 1657–1662
5. P. G. Grinevich, K. V. Kaipa, “Multiscale Limit for Finite-Gap Sine-Gordon Solutions and Calculation of Topological Charge Using Theta-Functional Formulae”, Proc. Steklov Inst. Math., 266 (2009), 49–58