We study the nonlinear
evolutionary euclidean bosonic string equation $$\begin{aligned} u_t = \Delta e^{-c \Delta }\,u + U(t,u) , \quad c > 0 \end{aligned}$$
on the Euclidean space
\({\mathbb {R}}^n\). We interpret the nonlocal operator
\(\Delta e^{-c\,\Delta }\) using entire vectors of
\(\Delta \) in
\(L^2({\mathbb {R}}^n)\). We prove that it generates a bounded holomorphic
\(C_0\)-semigroup on
\(L^2({\mathbb {R}}^n)\) (so that it also satisfies maximal
\(L^p\) regularity) and we show the well-posedness of the corresponding nonlinear Cauchy problem.