| Abstrakt: |
A survey is given of results concerning the structure of solutions of aone-dimensional non-linear pseudodifferential equation describingthe dynamics (rolling) of a $p$-adic open string for thescalar tachyon field. It is indicated that discontinuous solutionscan occur for $p=2$. The method of expanding the solutions inseries of Hermite polynomials and the method of reduction to anon-linear boundary-value problem for the heat equation are used.Some unsolved problems are given, in particular, the existenceproblem for a solution of the boundary-value problem for $p=2$. |
