The role of the massless phantom term in the stability of a non-topological soliton solution

Abstract: We intend to introduce classically a special Lagrangian density in such a way that, firstly, it leads to a special non-topological solitary wave solution, secondly, the stability of that is guaranteed properly, and thirdly, its dominant dynamical equations reduce to the standard nonlinear Klein-Gordon equations. For these purposes, we have to consider a new term in the Lagrangian density, whose role is like a massless phantom that surrounds the special solitary wave solution and resists any change in its internal structure.