# Stability Catalyzer for a Relativistic Non-Topological Soliton Solution

## TL;DR

This paper introduces a method to stabilize a specific solitary wave solution in a nonlinear Klein-Gordon system by adding a massless term, making it energetically stable and akin to stable particles.

## Contribution

It proposes a novel stability catalyzer by adding a massless term to the Lagrangian, ensuring the stability of the solitary wave solution without altering its fundamental dynamics.

## Key findings

- Adding the term guarantees energetic stability of the SSWS.
- Large parameter B enhances stability and prevents formation of non-trivial solutions with finite energy.
- Stable configurations resemble multiple isolated SSWSs, similar to particles.

## Abstract

For a real nonlinear Klein-Gordon Lagrangian density with a special solitary wave solution (SSWS), which is essentially unstable, it is shown how adding a proper additional massless term could guarantee the energetically stability of the SSWS, without changing its dominant dynamical equation and other properties. In other words, it is a stability catalyzer. The additional term contains a parameter $B$, which brings about more stability for the SSWS at larger values. Hence, if one considers $B$ to be an extremely large value, then any other solution which is not very close to the free far apart SSWSs and the trivial vacuum state, require an infinite amount of energy to be created. In other words, the possible non-trivial stable configurations of the fields with the finite total energies are any number of the far apart SSWSs, similar to any number of identical particles.