Mathematical Modeling of Soliton-like Solutions in the Scalar-tensor Theories of Gravity

In the present, work we find new numerical solutions describing soliton‐like objects coupled to non‐linear electrodynamics in the scalar‐tensor theories of gravity. Approximate solutions have been also obtained and a comparison to the numerical results has been made. The non‐existence of black holes for the specific choice of lagrangian of the nonlinear electrodynamics has been also proved.