RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Subscription Guidelines for authors License agreement Submit a manuscript Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 TMF: Year: Volume: Issue: Page: Find

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

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

DOI: https://doi.org/10.4213/tmf2043

Full text: PDF file (187 kB)
References: PDF file   HTML file

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

Bibliographic databases:

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
\Bibitem{Zhu06} \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 \mathnet{http://mi.mathnet.ru/tmf2043} \crossref{https://doi.org/10.4213/tmf2043} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2253626} \adsnasa{http://adsabs.harvard.edu/cgi-bin/bib_query?2006TMP...146..335J} \elib{http://elibrary.ru/item.asp?id=9200319} \transl \jour Theoret. and Math. Phys. \yr 2006 \vol 146 \issue 3 \pages 335--342 \crossref{https://doi.org/10.1007/s11232-006-0043-3} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000236533100004} \elib{http://elibrary.ru/item.asp?id=13529583} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33644926969} 

• http://mi.mathnet.ru/eng/tmf2043
• https://doi.org/10.4213/tmf2043
• http://mi.mathnet.ru/eng/tmf/v146/i3/p402

 SHARE:

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. 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
2. V. S. Vladimirov, “Nonlinear equations for $p$-adic open, closed, and open-closed strings”, Theoret. and Math. Phys., 149:3 (2006), 1604–1616
3. Joukovskaya, L, “Dynamics in nonlocal cosmological models derived from string field theory”, Physical Review D, 76:10 (2007), 105007
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
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
6. I. Ya. Aref'eva, I. V. Volovich, “The null energy condition and cosmology”, Theoret. and Math. Phys., 155:1 (2008), 503–511
7. Calcagni G, Nardelli G, “Nonlocal instantons and solitons in string models”, Physics Letters B, 669:1 (2008), 102–106
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
9. Barnaby N., Kamran N., “Dynamics with infinitely many derivatives: the initial value problem”, Journal of High Energy Physics, 2008, no. 2, 008
10. V. S. Vladimirov, “On Nonlinear Equations of $p$-adic Strings for Scalar Tachyon Fields”, Proc. Steklov Inst. Math., 265 (2009), 242–261
11. Calcagni, G, “Kinks of open superstring field theory”, Nuclear Physics B, 823:1-2 (2009), 234
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
13. Barnaby, N, “Dynamics and stability of light-like tachyon condensation”, Journal of High Energy Physics, 2009, no. 3, 018
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
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.
16. I. Ya. Aref'eva, “String field theory: From high energy to cosmology”, Theoret. and Math. Phys., 163:3 (2010), 697–704
17. Aref'eva I.Ya., Volovich I.V., “Cosmological daemon”, Journal of High Energy Physics, 2011, no. 8, 102
18. Aref'eva I., “Puzzles with Tachyon in SSFT and Cosmological Applications”, Progr Theoret Phys Suppl, 2011, no. 188, 29–40
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
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
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
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
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
24. Kh. A. Khachatryan, “On the solvability of a boundary value problem in $p$-adic string theory”, Trans. Moscow Math. Soc., 2018, 101–115
•  Number of views: This page: 746 Full text: 197 References: 53 First page: 1