Geodesic
Nonlinear equations for $p$-adic open, closed, and open-closed strings
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 3, pp. 354-367 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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V. S. Vladimirov. Nonlinear equations for $p$-adic open, closed, and open-closed strings. Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 3, pp. 354-367. http://geodesic.mathdoc.fr/item/TMF_2006_149_3_a2/

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