Solutions of the nonlinear Klein-Gordon equation and the generalized uncertainty principle with the hybrid analytical and numerical method

Abstract

Motivated by the prediction of a minimal measurable length at Planck scale found in many candidate theories of quantum gravity, we examine the Klein-Gordon equation with a $\lambda {\varphi }^4$ interaction and a symmetry-breaking term, in the presence of a generalized uncertainty principle associated with a minimal length. This allows us to assess the correction which underlying physical systems of scalar fields would undergo. Further, we solve the Euler-Lagrange equation by applying the Hybrid Analytical and Numerical (or HAN, for short) method, an effective approach for solving a large variety of nonlinear ordinary and partial differential equations.