Mathematical questions for theory of nonlinear pseudodifferential equations with $p$-adic string

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.