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

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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 149, Number 3, Pages 354–367
DOI: https://doi.org/10.4213/tmf5522 (Mi tmf5522)

This article is cited in 62 scientific papers (total in 62 papers)

Nonlinear equations for

p

$p$ -adic open, closed, and open-closed strings

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences

Full-text PDF (500 kB) Citations (62)

References:

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

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

$p$ -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

$p$ of the form

p = 4 n + 1

$p=4n+1$ under the condition that the solution for the closed string is known. For

p = 2

$p=2$ , 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.

Received: 16.06.2006

English version:
Theoretical and Mathematical Physics, 2006, Volume 149, Issue 3, Pages 1604–1616
DOI: https://doi.org/10.1007/s11232-006-0144-z

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. S. Vladimirov, “Nonlinear equations for

p

$p$ -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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Related presentations:

Nonlinear equations for $p$ -adic open and closed strings
V. S. Vladimirov, October 9, 2008 10:00

This publication is cited in the following 62 articles:

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Kh. A. Khachatryan, H. S. Petrosyan, “On qualitative properties of the solution of a boundary value problem for a system of nonlinear integral equations”, Theoret. and Math. Phys., 218:1 (2024), 145–162
A. Kh. Khachatryan, Kh. A. Khachatryan, A. S. Petrosyan, “Voprosy suschestvovaniya, otsutstviya i edinstvennosti resheniya odnogo klassa nelineinykh integralnykh uravnenii na vsei pryamoi s operatorom tipa Gammershteina — Ctiltesa”, Tr. IMM UrO RAN, 30, no. 1, 2024, 249–269
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H. S. Petrosyan, Kh. A. Khachatryan, “On the Solvability of an Infinite System of Algebraic Equations with Monotone and Concave Nonlinearity”, Sib Math J, 65:6 (2024), 1450
A. S. Petrosyan, S. M. Andriyan, Kh. A. Khachatryan, “Voprosy suschestvovaniya i edinstvennosti resheniya odnogo klassa beskonechnoi sistemy nelineinykh dvumernykh uravnenii”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 24:4 (2024), 498–511
H. S. Petrosyan, Kh. A. Khachatryan, “Uniqueness of the Solution of a Class of Integral Equations with Sum-Difference. Kernel and with Convex Nonlinearity on the Positive Half-Line”, Math. Notes, 113:4 (2023), 512–524
Kh. A. Khachatryan, A. S. Petrosyan, “Teoremy suschestvovaniya i edinstvennosti dlya odnoi beskonechnoi sistemy nelineinykh algebraicheskikh uravnenii”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 44 (2023), 44–54
A. Kh. Khachatryan, Kh. A. Khachatryan, H. S. Petrosyan, “On nonlinear convolution-type integral equations in the theory of $p$-adic strings”, Theoret. and Math. Phys., 216:1 (2023), 1068–1081
Kh. A. Khachatryan, A. S. Petrosyan, “O razreshimosti odnogo klassa nelineinykh dvumernykh integralnykh uravnenii tipa Gammershteina–Nemytskogo na ploskosti”, Vestn. Sam. gos. tekhn. un-ta. Ser. Fiz.-mat. nauki, 27:3 (2023), 446–461
A.Kh. Khachatryan, Kh.A. Khachatryan, “ON QUALITATIVE PROPERTIES OF A SOLUTION OF ONE CLASS SINGULAR INTEGRAL EQUATIONS ON THE WHOLE LINE WITH ODD NONLINEARITY”, J Math Sci, 271:5 (2023), 597
Kh. A. Khachatryan, H. S. Petrosyan, S. M. Andriyan, “On the solubility of a class of two-dimensional integral equations on a quarter plane with monotone nonlinearity”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2022, no. 2, 19–38
Ivan Kolář, “Nonlocal scalar fields in static spacetimes via heat kernels”, Phys. Rev. D, 105:8 (2022)
Kh. A. Khachatryan, H. S. Petrosyan, “On the Constructive Solvability of a Two-Dimensional Nonlinear Integral Equation Arising in the Theory of $p$-Adic Strings”, P-Adic Num Ultrametr Anal Appl, 14:S1 (2022), S74
Kh. A. Khachatryan, H. S. Petrosyan, “Solvability of a certain system of singular integral equations with convex nonlinearity on the positive half-line”, Russian Math. (Iz. VUZ), 65:1 (2021), 27–46

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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