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TMF, 2006, Volume 146, Number 3, Pages 402–409 (Mi tmf2043)  

This article is cited in 27 scientific papers (total in 27 papers)

Iterative method for solving nonlinear integral equations describing rolling solutions in string theory

L. V. Zhukovskaya

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the properties of this equation, construct an iterative method for solving it, and prove that the method converges.

Keywords: string theory, nonlinear integral equation, iterative method


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English version:
Theoretical and Mathematical Physics, 2006, 146:3, 335–342

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Received: 21.04.2005
Revised: 17.08.2005

Citation: L. V. Zhukovskaya, “Iterative method for solving nonlinear integral equations describing rolling solutions in string theory”, TMF, 146:3 (2006), 402–409; Theoret. and Math. Phys., 146:3 (2006), 335–342

Citation in format AMSBIB
\by L.~V.~Zhukovskaya
\paper Iterative method for solving nonlinear integral equations describing rolling solutions in string theory
\jour TMF
\yr 2006
\vol 146
\issue 3
\pages 402--409
\jour Theoret. and Math. Phys.
\yr 2006
\vol 146
\issue 3
\pages 335--342

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    This publication is cited in the following articles:
    1. V. S. Vladimirov, “On the non-linear equation of a $p$-adic open string for a scalar field”, Russian Math. Surveys, 60:6 (2005), 1077–1092  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. V. S. Vladimirov, “Nonlinear equations for $p$-adic open, closed, and open-closed strings”, Theoret. and Math. Phys., 149:3 (2006), 1604–1616  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Joukovskaya, L, “Dynamics in nonlocal cosmological models derived from string field theory”, Physical Review D, 76:10 (2007), 105007  crossref  mathscinet  adsnasa  isi  elib  scopus  scopus
    4. Aref'eva I.Ya., Joukovskaya L.V., “Bouncing and accelerating solutions in nonlocal stringy models”, Journal of High Energy Physics, 2007, no. 7, 087  crossref  mathscinet  isi  scopus  scopus
    5. Joukovskaya L., “Dynamics With Infinite Number of Derivatives for Level Truncated Non-Commutative Interaction”, Quantum Probability and Infinite Dimensional Analysis, Proceedings, Qp-Pq Quantum Probability and White Noise Analysis, 20, 2007, 258–266  crossref  mathscinet  zmath  isi
    6. I. Ya. Aref'eva, I. V. Volovich, “The null energy condition and cosmology”, Theoret. and Math. Phys., 155:1 (2008), 503–511  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Calcagni G, Nardelli G, “Nonlocal instantons and solitons in string models”, Physics Letters B, 669:1 (2008), 102–106  crossref  mathscinet  adsnasa  isi  elib  scopus
    8. Aref'eva IY, Joukovskaya LV, Vernov SY, “Dynamics in nonlocal linear models in the Friedmann-Robertson-Walker metric”, Journal of Physics A-Mathematical and Theoretical, 41:30 (2008), 304003  crossref  mathscinet  zmath  isi  scopus  scopus
    9. Barnaby N., Kamran N., “Dynamics with infinitely many derivatives: the initial value problem”, Journal of High Energy Physics, 2008, no. 2, 008  crossref  mathscinet  isi  scopus  scopus
    10. V. S. Vladimirov, “On Nonlinear Equations of $p$-adic Strings for Scalar Tachyon Fields”, Proc. Steklov Inst. Math., 265 (2009), 242–261  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    11. Calcagni, G, “Kinks of open superstring field theory”, Nuclear Physics B, 823:1-2 (2009), 234  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    12. Aref'eva, IY, “Pure gauge configurations and tachyon solutions to string field theories equations of motion”, Journal of High Energy Physics, 2009, no. 5, 050  crossref  mathscinet  isi  scopus  scopus
    13. Barnaby, N, “Dynamics and stability of light-like tachyon condensation”, Journal of High Energy Physics, 2009, no. 3, 018  crossref  isi  scopus  scopus
    14. Joukovskaya L., “Dynamics with infinitely many time derivatives in Friedmann-Robertson-Walker background and rolling tachyons”, Journal of High Energy Physics, 2009, no. 2, 045  crossref  mathscinet  zmath  isi  scopus  scopus
    15. Vernov S.Yu., “Localization of nonlocal cosmological models with quadratic potentials in the case of double roots”, Classical and Quantum Gravity, 27:3 (2010), 035006, 16 pp.  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    16. I. Ya. Aref'eva, “String field theory: From high energy to cosmology”, Theoret. and Math. Phys., 163:3 (2010), 697–704  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    17. Aref'eva I.Ya., Volovich I.V., “Cosmological daemon”, Journal of High Energy Physics, 2011, no. 8, 102  crossref  zmath  isi  scopus  scopus
    18. Aref'eva I., “Puzzles with Tachyon in SSFT and Cosmological Applications”, Progr Theoret Phys Suppl, 2011, no. 188, 29–40  crossref  zmath  adsnasa  isi  scopus  scopus
    19. Kh. A. Khachatryan, “On the solubility of certain classes of non-linear integral equations in $p$-adic string theory”, Izv. Math., 82:2 (2018), 407–427  mathnet  crossref  crossref  adsnasa  isi  elib
    20. Khachatryan A.Kh., Khachatryan Kh.A., “Solvability of a Class of Nonlinear Pseudo-Differential Equations in R-N”, P-Adic Numbers Ultrametric Anal. Appl., 10:2 (2018), 90–99  crossref  mathscinet  isi  scopus  scopus
    21. Khachatryan Kh.A., Terjyan Ts.E., Avetisyan M.H., “A One-Parameter Family of Bounded Solutions For a System of Nonlinear Integral Equations on the Whole Line”, J. Contemp. Math. Anal.-Armen. Aca., 53:4 (2018), 201–211  crossref  isi  scopus
    22. Kh. A. Khachatryan, A. S. Petrosyan, M. O. Avetisyan, “Voprosy razreshimosti odnogo klassa nelineinykh integralnykh uravnenii tipa svertki v $\mathbb {R}^n$”, Tr. IMM UrO RAN, 24, no. 3, 2018, 247–262  mathnet  crossref  elib
    23. A. Kh. Khachatryan, Kh. A. Khachatryan, “Solvability of a nonlinear integral equation in dynamical string theory”, Theoret. and Math. Phys., 195:1 (2018), 529–537  mathnet  crossref  crossref  adsnasa  isi  elib
    24. Kh. A. Khachatryan, “On the solvability of a boundary value problem in $ p$-adic string theory”, Trans. Moscow Math. Soc., 2018, 101–115  mathnet  crossref  elib
    25. Kh. A. Khachatryan, “O razreshimosti odnoi sistemy nelineinykh integralnykh uravnenii tipa Gammershteina na pryamoi”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 19:2 (2019), 164–181  mathnet  crossref  elib
    26. Kh. A. Khachatryan, A. S. Petrosyan, “O postroenii summiruemogo resheniya odnogo klassa nelineinykh integralnykh uravnenii tipa Gammershteina - Nemytskogo na vsei pryamoi”, Tr. IMM UrO RAN, 26, no. 2, 2020, 278–287  mathnet  crossref  elib
    27. Kh. A. Khachatryan, “Existence and uniqueness of solution of a certain boundary-value problem for a convolution integral equation with monotone non-linearity”, Izv. Math., 84:4 (2020), 807–815  mathnet  crossref  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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