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TMF, 2006, Volume 149, Number 3, Pages 354–367 (Mi tmf5522)  

This article is cited in 28 scientific papers (total in 28 papers)

Nonlinear equations for $p$-adic open, closed, and open-closed strings

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We investigate the structure of solutions of boundary value problems for a one-dimensional nonlinear system of pseudodifferential equations describing the dynamics {(}rolling{\rm)} of $p$-adic open, closed, and open-closed strings for a scalar tachyon field using the method of successive approximations. For an open-closed string, we prove that the method converges for odd values of $p$ of the form $p=4n+1$ under the condition that the solution for the closed string is known. For $p=2$, we discuss the questions of the existence and the nonexistence of solutions of boundary value problems and indicate the possibility of discontinuous solutions appearing.

Keywords: string, tachyon

DOI: https://doi.org/10.4213/tmf5522

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English version:
Theoretical and Mathematical Physics, 2006, 149:3, 1604–1616

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Received: 16.06.2006

Citation: V. S. Vladimirov, “Nonlinear equations for $p$-adic open, closed, and open-closed strings”, TMF, 149:3 (2006), 354–367; Theoret. and Math. Phys., 149:3 (2006), 1604–1616

Citation in format AMSBIB
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    1. 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
    2. V. S. Vladimirov, “The question of the asymptotic behavior as $|t|\to\infty$ of boundary value problem solutions for $p$-adic strings”, Theoret. and Math. Phys., 157:3 (2008), 1638–1645  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    3. B. G. Dragovich, “Zeta-nonlocal scalar fields”, Theoret. and Math. Phys., 157:3 (2008), 1671–1677  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
    5. Calcagni G, Montobbio M, Nardelli G, “Localization of nonlocal theories”, Physics Letters B, 662:3 (2008), 285–289  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. Vladimirov VS, “The equation of the p-adic closed strings for the scalar tachyon field”, Science in China Series A-Mathematics, 51:4 (2008), 754–764  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Dragovich B, “Lagrangians with Riemann zeta function”, Romanian Journal of Physics, 53:9–10 (2008), 1105–1110  mathscinet  zmath  isi
    8. Barnaby N., Kamran N., “Dynamics with infinitely many derivatives: variable coefficient equations”, Journal of High Energy Physics, 2008, no. 12, 022  crossref  mathscinet  zmath  isi  scopus
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    10. Barnaby, N, “Dynamics and stability of light-like tachyon condensation”, Journal of High Energy Physics, 2009, no. 3, 018  crossref  isi  scopus
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    12. Calcagni, G, “Kinks of open superstring field theory”, Nuclear Physics B, 823:1–2 (2009), 234  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    13. 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
    14. Calcagni G., Nardelli G., “String theory as a diffusing system”, Journal of High Energy Physics, 2010, no. 2, 093  crossref  mathscinet  zmath  isi  scopus
    15. Calcagni G., Nardelli G., “Nonlocal gravity and the diffusion equation”, Phys Rev D, 82:12 (2010), 123518  crossref  mathscinet  adsnasa  isi  elib  scopus
    16. V. S. Vladimirov, “Matematicheskie voprosy teorii nelineinykh psevdodifferentsialnykh uravnenii $p$-adicheskikh strun”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 1(22) (2011), 34–41  mathnet  crossref  elib
    17. V. S. Vladimirov, “Nonexistence of solutions of the $p$-adic strings”, Theoret. and Math. Phys., 174:2 (2013), 178–185  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. Calcagni G. Modesto L. Nicolini P., “Super-Accelerating Bouncing Cosmology in Asymptotically Free Non-Local Gravity”, Eur. Phys. J. C, 74:8 (2014), 2999  crossref  adsnasa  isi  scopus
    19. Khachatryan Kh.A., “On Solvability of One Class of Nonlinear Integral Equations on Whole Line With a Weak Singularity At Zero”, P-Adic Numbers Ultrametric Anal. Appl., 9:4 (2017), 292–305  crossref  mathscinet  zmath  isi  scopus
    20. Dragovich B. Khrennikov A.Yu. Kozyrev S.V. Volovich I.V. Zelenov E.I., “P-Adic Mathematical Physics: the First 30 Years”, P-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121  crossref  mathscinet  zmath  isi  scopus
    21. Calcagni G., “String Theory”: G. Calcagni, Classical and Quantum Cosmology, Graduate Texts in Physics, Springer International Publishing Ag, 2017, 625–700  crossref  mathscinet  isi
    22. 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
    23. 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
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    26. 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
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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