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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 3, Pages 55–80 (Mi izv640)  

This article is cited in 37 scientific papers (total in 37 papers)

The equation of the $p$-adic open string for the scalar tachyon field

V. S. Vladimirov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We study the structure of solutions of the one-dimensional non-linear pseudodifferential equation describing the dynamics of the $p$-adic open string for the scalar tachyon field $p^{\frac12\partial^2_t}\Phi=\Phi^p$. We explain the role of real zeros of the entire function $\Phi^p(z)$ and the behaviour of solutions $\Phi(t)$ in the neighbourhood of these zeros. We point out that discontinuous solutions can appear if $p$ is even. We use the method of expanding the solution $\Phi$ and the function $\Phi^p$ in Hermite polynomials and modified Hermite polynomials and establish a connection between the coefficients of these expansions (integral conservation laws). For $p=2$ we construct an infinite system of non-linear equations in the unknown Hermite coefficients and study its structure. We consider the 3-approximation. We indicate a connection between the problems stated and a non-linear boundary-value problem for the heat equation.

DOI: https://doi.org/10.4213/im640

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English version:
Izvestiya: Mathematics, 2005, 69:3, 487–512

Bibliographic databases:

Document Type: Article
UDC: 517.958+530.1
MSC: 46S10, 81-02
Received: 13.01.2005

Citation: V. S. Vladimirov, “The equation of the $p$-adic open string for the scalar tachyon field”, Izv. RAN. Ser. Mat., 69:3 (2005), 55–80; Izv. Math., 69:3 (2005), 487–512

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    2. L. V. Zhukovskaya, “Iterative method for solving nonlinear integral equations describing rolling solutions in string theory”, Theoret. and Math. Phys., 146:3 (2006), 335–342  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    3. 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
    4. Koshelev A.S., “Non-local SFT tachyon and cosmology”, J. High Energy Phys., 2007, no. 4, 029, 19 pp.  crossref  mathscinet  isi  elib
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    9. Górka P., Prado H., Reyes E.G., “Nonlinear equations with infinitely many derivatives”, Complex Anal. Oper. Theory, 2009  crossref  mathscinet  isi
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