Geodesic
Mathematical questions for theory of nonlinear pseudodifferential equations with $p$-adic string
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 34-41.

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This work is devoted to the mathematical description of the dynamics of tachyons of open, closed and open-closed $p$-adic strings. The questions of existence and nonexistence of continuous solutions and their properties, as well zero structure of solutions is discussed. New multidimensional nonlinear equations of ultraparabolic type are obtained. Some unsolved problems are listed.
Keywords: $p$-adic strings, nonlinear pseudodifferential equations, existence and continuity of solutions
Mots-clés : zero structure of solutions. 
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V. S. Vladimirov. Mathematical questions for theory of nonlinear pseudodifferential equations with $p$-adic string. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2011), pp. 34-41. http://geodesic.mathdoc.fr/item/VSGTU_2011_1_a4/

[1] Brekke L., Freund P. G. O., “p-Adic Numbers in Physics”, Phys. Rep. (Rev. Set. Phys. Lett.), 233:1 (1993), 1–66 | MR

[2] Moeller N., Schnabl M., “Tachyon condensation in open-closed $p$-adic string theory”, J. High Energy Phys., 2004, no. 1, 011, 18 pp. | DOI | MR | Zbl

[3] Vladimirov V. S., “Nonlinear equations for p-adic open, closed, and open-closed strings”, Theoret. and Math. Phys., 149:3 (2006), 1604–1616 | DOI | DOI | MR | Zbl

[4] Gelfand I. M., Shilov G. E., Generalized functions, v. 2, Spaces of fundamental and generalized functions, Fizmatlit, Moscow, 1958, 307 pp. | MR | Zbl

[5] Vladimirov V. S., Volovich Ya. I., “Nonlinear Dynamics Equation in $p$-Adic String Theory”, Theoret. and Math. Phys., 138:3 (2004), 297–309, arXiv: math-ph/0306018 | DOI | DOI | MR | Zbl

[6] Green M. B., Schwarz J., Witten E., Superstring theory, v. 1, Cambridge Monographs on Mathematical Physics, Introduction, Cambridge University Press, Cambridge, 1987, 469 pp. ; Grin M., Shvarts Dzh., Vitten E., Teoriya superstrun, v. I, Vvedenie, Mir, M., 1990, 518 pp. ; Green M. B., Schwarz J., Witten E., Superstring theory, v. 2, Cambridge Monographs on Mathematical Physics, Loop amplitudes, anomalies and phenomenology, Cambridge University Press, Cambridge, 1987, 596 pp. ; Grin M., Shvarts Dzh., Vitten E., Teoriya superstrun, v. II, Petlevye amplitudy, anomalii i fenomenologiya, Mir, M., 1990, 656 pp. | MR | Zbl | MR | MR | MR

[7] Brekke L., Freund P. G. O., Olson M., Witten E., “Non-Archimedian string dynamics”, Nuclear Phys. B, 302:3 (1988), 365–402 | DOI | MR

[8] Frampton P. H., Okada Y., “Effective scalar field theory of p-adic string”, Phys. Rev. D (3), 37:10 (1989), 3077–3079 | DOI | MR

[9] Vladimirov V. S., Volovich I. V., Zelenov E. I., $p$-Adic analysis and mathematical physics, v. 1, Series on Soviet and East European Mathematics, World Scientific Publishing Co., Inc., Singapore, 1994, 319 pp. | MR | MR | Zbl | Zbl

[10] Aref'eva I. Ja., Joukovskaja L. V., Koshelev A. S., “Time evolution in superstring field theory on non-BPS brane. I. Rolling tachyon and energy-momentum conservation”, J. High Energy Phys., 2003, no. 9, 012, 15 pp., arXiv: hep-th/0301137 | DOI | MR

[11] Aref'eva I. Ya., “Nonlocal string tachyon as a model for cosmological dark energy”, AIP Conf. Proc., 826, Amer. Inst. Phys., Melville, NY, 2006, 301–311, arXiv: astro-ph/0410443 | DOI | MR | Zbl

[12] Calcagni G., “Cosmological tachyon from cubic string field theory”, J. High Energy Phys., 2006, no. 5, 012, 25 pp., arXiv: hep-th/0512259 | DOI | MR

[13] Vladimirov V. S., “On the non-linear equation of ap-adic open string for a scalar field”, Russian Math. Surveys, 60:6 (2005), 1077–1092 | DOI | DOI | MR | Zbl

[14] Moeller N., Zwiebach B., “Dynamics with infinitely many time derivatives and rolling tachyons”, J. High Energy Phys., 2002, no. 10, 034, 39 pp., arXiv: hep-th/0207107 | DOI | MR

[15] Sen A., “Rolling Tachyon”, J. High Energy Phys., 2002, no. 4, 048, 18 pp., arXiv: hep-th/0203211 | DOI | MR

[16] Ghoshal D., Sen A., “Tachyon condensation and brane descent relations in $p$-adic string theory”, Nuclear Phys. B, 584:1–2 (2000), 300–312 | DOI | MR | Zbl

[17] Volovich I. V., “$p$-Adic string”, Class. Quantum Grav., 4:4 (1987), L83–L87 | DOI | MR

[18] Minahan J. A., “Mode Interactions of the Tachyon Condensate in $p$-Adic String Theory”, J. High Energy Phys., 2001, no. 3, 028, 16 pp. | DOI | MR

[19] Barnaby N., “Caustic formation in tachyon effective field theories”, J. High Energy Phys., 2004, no. 7, 025, 23 pp., arXiv: hep-th/0406120 | DOI | MR

[20] Coletti E., Sigalov I., Taylor W., “Taming the Tachion in Cubic String Field Theory”, J. High Energy Phys., 2005, no. 8, 104, 25 pp., arXiv: hep-th/0505031 | DOI | MR

[21] Vladimirov V. S., “The equation of the $ p$-adic open string for the scalar tachyon field”, Izv. Math., 69:3 (2005), 487–512, arXiv: math-ph/0507018 | DOI | DOI | MR | Zbl

[22] Vladimirov V. S., “The equation of the $p$-adic closed strings for the scalar tachion field”, Sci. China, Ser. A, 81:4 (2008), 754–764 | DOI | MR

[23] Vladimirov V. S., “On the Equations for $p$-Adic Closed and Open Strings”, $p$-Adic Numbers, Ultrametric Analysis and Applications, 1:1 (2009), 79–87 | DOI | MR | Zbl

[24] Vladimirov V. S., “On nonlinear equations of p-adic strings for scalar tachyon fields”, Proc. Steklov Inst. Math., 265 (2009), 242–261 | DOI | MR | Zbl