Introducing a relativistic nonlinear field system with a single stable non-topological soliton solution in 1+1 dimensions

Abstract

In this paper we present a new extended complex nonlinear Klein-Gordon Lagrangian density, which bears a single non-topological soliton solution with a specific rest frequency ω s in 1 + 1 dimensions. There is a proper term in the new Lagrangian density, which behaves like a massless spook that surrounds the single soliton solution and opposes any internal changes. In other words, any arbitrary variation in the single soliton solution leads to an increase in the total energy. Moreover, just for the single soliton solution, the general dynamical equations are reduced to those versions of a special type of the standard well-known complex nonlinear Klein-Gordon systems, as its dominant dynamical equations. * physmohammadi@pgu.ac.ir 1 arXiv:1902.02648v5 [physics.class-ph]

An energetically stable Q-ball solution in 3 + 1 dimensions

“…There is another stability criterion, called the energetically stability criterion [51]. If for a solitary wave solution, any arbitrary (permissible or impermissible) deformation above the background of that leads to an increase in the total energy, it would be indeed energetically a stable solution.…”

“…In other words, an energetically stable solitary wave solution has the minimum rest energy among the other (close) solutions. In this case, unlike the Vakhitov-Kolokolov criterion [39][40][41][42][43][44][45][46][47][48][49][50], we examine the energy density functional for the small variations instead of dynamical equations [51][52][53][54]. In general, none of the Q-ball solutions are energetically stable objects [51].…”

“…In this paper along with [51,52], we are going to introduce an extended KG system 1 in 3 + 1 dimensions which leads to a special energetically stable Q-ball solution. We show that the general dynamical equations, just for this special Q-ball solution, are reduced to the known versions of a special CNKG system, as its dominant dynamical equations.…”

“…We show that the general dynamical equations, just for this special Q-ball solution, are reduced to the known versions of a special CNKG system, as its dominant dynamical equations. In [51,52], there were introduced extended KG systems which lead to special Q-ball solutions in 1 + 1 dimensions. The main idea was to add a proper additional term F to the original standard CNKG Lagrangian density, which guarantees the uniqueness and energetically stability of one of its Q-ball solutions.…”

“…The main idea was to add a proper additional term F to the original standard CNKG Lagrangian density, which guarantees the uniqueness and energetically stability of one of its Q-ball solutions. However, to bring this idea to life in 3 + 1 dimensions, unlike the pervious works in 1 + 1 dimensions [51,52], we have to reintroduce the additional term F using three new scalar catalyzer fields ψ 1 , ψ 2 and ψ 3 , whose roles in dominant dynamical equations and other observable of the special Q-ball solution are ineffective. In fact, these catalyzer fields ψ j (j = 1, 2, 3) must be included in the additional term F to play the expected roles properly.…”