Non-Classical Traveling Solutions in a Nonlinear Klein Gordon Model

A model with interparticle inharmonic interaction under the Φ⁴ external potential is studied. Making use of the special relation of relevant parameters, in the continuous limit, it was possible to obtain various non-classical soliton solutions, specifically, compact and peak-like solutions. The solutions undergo a jump on their first derivatives at some points of the space-time manifold. These analytic solutions were obtained by considering strong restrictions on their velocities and on the jump conditions. The energy concentrated in these solutions shows in several cases a discrete spectrum.