Nonlinear equations for $p$-adic open, closed, and open-closed strings
Teoretičeskaâ i matematičeskaâ fizika, Tome 149 (2006) no. 3, pp. 354-367
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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.
@article{TMF_2006_149_3_a2,
author = {V. S. Vladimirov},
title = {Nonlinear equations for $p$-adic open, closed, and open-closed strings},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {354--367},
publisher = {mathdoc},
volume = {149},
number = {3},
year = {2006},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2006_149_3_a2/}
}
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/