  We propose here a static and axisymmetric braneworld in six dimensions as a
string-like model extension. For a subtle warp function, this scenario provides
near brane corrections. By varying the bulk cosmological constant, we obtain a
source which passes through different phases. The solution is defined both for
the interior as for the exterior of the string and satisfies the weak energy
condition. Smooth gravitational massless mode is localized on the brane which
core is displaced from the origin. In contrast to the thin string model, the
massive solutions have high amplitude near the brane. By means of an analogue
quantum potential analysis, we show that s-waves gravitational Kaluza-Klein
modes are permissible as resonant states.
