  In the framework of the relativistic generalized uncertainty principle
(RGUP), we study the nonlinear Klein-Gordon field with $\phi^4$
self-interaction. This generalization comes from the quantum gravity theories
that predict the existence of a minimal measurable length scale. The quantum
gravity effects slightly modify the momentum and change the Lagrangian density
of the field. This model, specifically in the context of spontaneous symmetry
breaking, is so fruitful and leads us to many interesting phenomena. Due to the
complexity of the consequent equations, the model is normally studied via
perturbation mechanisms. However, here, we apply a generalized $tanh$-method
which supposed that the field solutions should be $sech$-functions of segments
of space and time. By this extended method, we find some more general solutions
with respect to our previous work \cite{Mir1}. Several solutions can be found
but we select only the normalizable and bounded solitary fields. The energy
spectrum of each field solution is obtained in an analytical form and
discussed. The modification parameter of the corresponding RGUP is estimated by
using the rest energy of the mass of the Higgs boson.
