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- W3102527720 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 $p^{frac12partial^2_t}Phi=Phi^p$. We elicit 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 the 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 the non-linear boundary-value problem for the heat equation." @default.
- W3102527720 created "2020-11-23" @default.
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- W3102527720 date "2005-06-30" @default.
- W3102527720 modified "2023-10-18" @default.
- W3102527720 title "The equation of the $ p$-adic open string for the scalar tachyon field" @default.
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- W3102527720 doi "https://doi.org/10.1070/im2005v069n03abeh000536" @default.
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