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

This article is cited in 25 scientific papers (total in 25 papers)

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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Received: 16.04.1979

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
\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
\jour Theoret. and Math. Phys.
\yr 1979
\vol 40
\issue 2
\pages 706--715

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    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  mathnet  crossref  mathscinet  zmath  isi
    2. S. A. Vladimirov, “Automorphic systems of scalar fields”, Theoret. and Math. Phys., 46:1 (1981), 28–32  mathnet  crossref  mathscinet  zmath  isi
    3. A. P. Veselov, “Dynamics of the singularities of solutions of some nonlinear equations”, Theoret. and Math. Phys., 50:3 (1982), 314–316  mathnet  crossref  mathscinet  zmath  isi
    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  mathnet  crossref  mathscinet  isi
    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  mathnet  crossref  mathscinet  isi
    6. B. A. Putko, “Reduction of Kählerian chiral model”, Theoret. and Math. Phys., 50:1 (1982), 69–75  mathnet  crossref  mathscinet  isi
    7. G. P. Jorjadze, “Hamiltonian description of singular solutions of the Liouville equation”, Theoret. and Math. Phys., 65:3 (1985), 1189–1195  mathnet  crossref  mathscinet  zmath  isi
    8. S. V. Talalov, “Singular solutions of the Liouville equation on an interval”, Theoret. and Math. Phys., 67:3 (1986), 537–545  mathnet  crossref  mathscinet  zmath  isi
    9. S. V. Talalov, “Hamiltonian structure of “thirring$\times$liouville” model. Singular solutions”, Theoret. and Math. Phys., 71:3 (1987), 588–597  mathnet  crossref  mathscinet  zmath  isi
    10. A. Yu. Volkov, “Miura transformation on a lattice”, Theoret. and Math. Phys., 74:1 (1988), 96–99  mathnet  crossref  mathscinet  zmath  isi
    11. Theoret. and Math. Phys., 92:3 (1992), 979–987  mathnet  crossref  mathscinet  zmath  isi
    12. Theoret. and Math. Phys., 104:1 (1995), 892–920  mathnet  crossref  mathscinet  zmath  isi
    13. S. V. Klimenko, I. N. Nikitin, “Singularities on world sheets of open relativistic strings”, Theoret. and Math. Phys., 114:3 (1998), 299–312  mathnet  crossref  crossref  mathscinet  zmath  isi
    14. G. P. Jorjadze, W. Piechocki, “A relativistic particle in the Liouville field”, Theoret. and Math. Phys., 118:2 (1999), 183–196  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. L. A. Kalyakin, “Perturbation of a singular solution to the Liouville equation”, Theoret. and Math. Phys., 118:3 (1999), 307–313  mathnet  crossref  crossref  mathscinet  zmath  isi
    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  crossref  isi
    17. L. A. Kalyakin, “Asymptotic decay of solutions of the Liouville equation under perturbations”, Math. Notes, 68:2 (2000), 173–184  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    18. S. V. Talalov, “Geometric description of a relativistic string”, Theoret. and Math. Phys., 123:1 (2000), 446–450  mathnet  crossref  crossref  mathscinet  zmath  isi
    19. Jorjadze, G, “Poisson structure and Moyal quantisation of the Liouville theory”, Nuclear Physics B, 619:1–3 (2001), 232  crossref  isi
    20. Kalyakin, LA, “Liouville equation under perturbation”, Inverse Problems, 17:4 (2001), 879  crossref  isi
    21. Bernal, J, “Soliton-like structures and the connection between the Bq and KP equations”, Chaos Solitons & Fractals, 17:5 (2003), 951  crossref  isi
    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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. S. V. Talalov, “Description of braids in terms of first-order spectral problems”, Theoret. and Math. Phys., 159:1 (2009), 469–473  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    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  isi
    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  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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