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 TMF, 1979, Volume 40, Number 2, Pages 221–234 (Mi tmf2889)

Singular solutions of the equation $\Box\varphi+(m^2/2)\exp\varphi=0$ and dynamics of singularities

G. P. Jorjadze, A. K. Pogrebkov, M. K. Polivanov

Abstract: Solutions of the Liouville equation with singularities are studied. The solutions are interpreted geometrically and their topological invariants found. Dynamical systems describing the motion of singularities are considered. Some simple examples are described in detail.

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English version:
Theoretical and Mathematical Physics, 1979, 40:2, 706–715

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Citation: G. P. Jorjadze, A. K. Pogrebkov, M. K. Polivanov, “Singular solutions of the equation $\Box\varphi+(m^2/2)\exp\varphi=0$ and dynamics of singularities”, TMF, 40:2 (1979), 221–234; Theoret. and Math. Phys., 40:2 (1979), 706–715

Citation in format AMSBIB
\Bibitem{JorPogPol79} \by G.~P.~Jorjadze, A.~K.~Pogrebkov, M.~K.~Polivanov \paper Singular solutions of the equation $\Box\varphi+(m^2/2)\exp\varphi=0$ and dynamics of singularities \jour TMF \yr 1979 \vol 40 \issue 2 \pages 221--234 \mathnet{http://mi.mathnet.ru/tmf2889} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=549616} \zmath{https://zbmath.org/?q=an:0415.35053} \transl \jour Theoret. and Math. Phys. \yr 1979 \vol 40 \issue 2 \pages 706--715 \crossref{https://doi.org/10.1007/BF01018719} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JG19600004} 

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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. A. K. Pogrebkov, “Complete integrability of dynamical systems generated by singular solutions of liouville's equation”, Theoret. and Math. Phys., 45:2 (1980), 951–957
2. S. A. Vladimirov, “Automorphic systems of scalar fields”, Theoret. and Math. Phys., 46:1 (1981), 28–32
3. A. P. Veselov, “Dynamics of the singularities of solutions of some nonlinear equations”, Theoret. and Math. Phys., 50:3 (1982), 314–316
4. A. A. Zheltukhin, “Classical relativistic string as a two-dimensional $SO(1,1)\times SO(2)$ gauge model”, Theoret. and Math. Phys., 52:1 (1982), 666–675
5. V. A. Arkad'ev, A. K. Pogrebkov, M. K. Polivanov, “Application of inverse scattering method to singular solutions of nonlinear equations. I”, Theoret. and Math. Phys., 53:2 (1982), 1051–1062
6. B. A. Putko, “Reduction of Kählerian chiral model”, Theoret. and Math. Phys., 50:1 (1982), 69–75
7. G. P. Jorjadze, “Hamiltonian description of singular solutions of the Liouville equation”, Theoret. and Math. Phys., 65:3 (1985), 1189–1195
8. S. V. Talalov, “Singular solutions of the Liouville equation on an interval”, Theoret. and Math. Phys., 67:3 (1986), 537–545
9. S. V. Talalov, “Hamiltonian structure of “thirring$\times$liouville” model. Singular solutions”, Theoret. and Math. Phys., 71:3 (1987), 588–597
10. A. Yu. Volkov, “Miura transformation on a lattice”, Theoret. and Math. Phys., 74:1 (1988), 96–99
11. Theoret. and Math. Phys., 92:3 (1992), 979–987
12. Theoret. and Math. Phys., 104:1 (1995), 892–920
13. S. V. Klimenko, I. N. Nikitin, “Singularities on world sheets of open relativistic strings”, Theoret. and Math. Phys., 114:3 (1998), 299–312
14. G. P. Jorjadze, W. Piechocki, “A relativistic particle in the Liouville field”, Theoret. and Math. Phys., 118:2 (1999), 183–196
15. L. A. Kalyakin, “Perturbation of a singular solution to the Liouville equation”, Theoret. and Math. Phys., 118:3 (1999), 307–313
16. Zloshchastiev, KG, “Zero-brane approach to the study of particle-like solitons in classical and quantum Liouville field theory”, Journal of Physics G-Nuclear and Particle Physics, 25:11 (1999), 2177
17. L. A. Kalyakin, “Asymptotic decay of solutions of the Liouville equation under perturbations”, Math. Notes, 68:2 (2000), 173–184
18. S. V. Talalov, “Geometric description of a relativistic string”, Theoret. and Math. Phys., 123:1 (2000), 446–450
19. Jorjadze, G, “Poisson structure and Moyal quantisation of the Liouville theory”, Nuclear Physics B, 619:1–3 (2001), 232
20. Kalyakin, LA, “Liouville equation under perturbation”, Inverse Problems, 17:4 (2001), 879
21. Bernal, J, “Soliton-like structures and the connection between the Bq and KP equations”, Chaos Solitons & Fractals, 17:5 (2003), 951
22. V. De Alfaro, A. T. Filippov, “Dimensional reduction of gravity and relation between static states, cosmologies, and waves”, Theoret. and Math. Phys., 153:3 (2007), 1709–1731
23. S. V. Talalov, “Description of braids in terms of first-order spectral problems”, Theoret. and Math. Phys., 159:1 (2009), 469–473
24. Jorjadze, G, “Singular Liouville fields and spiky strings in R-1,R-2 and SL(2, R)”, Journal of High Energy Physics, 2009, no. 10, 092
25. Talalov S.V., “Planar String as an Anyon Model: Cusps, Braids and Soliton Exitations”, 7th International Conference on Quantum Theory and Symmetries (Qts7), Journal of Physics Conference Series, 343, IOP Publishing Ltd, 2012, 012121
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