Normal-mode diagonalization for two-component topological kinks

Abstract

We present a linear-stability analysis for the kink solutions of a two-component nonlinear scalar model in (1+1)dimensions. The study follows the traditional approaches which directly treat the normal-mode problem.The classical solutions of nonlinear-field theories exhib-

Soliton stability in systems of two real scalar fields

“…Furthermore, the solutions are very similar to the pairs of classical configurations investigated in [8], and so it seems interesting to compare the present calculations with the ones there introduced. Here we recall that we already know that the above pairs of solutions are stable [2,4], while the pairs considered in [8] were shown to be unstable, at least in the region of parameters there considered.…”

“…In that investigation, it was also shown [8] that when the parameters of the system allows for a normal mode diagonalization that leads to analytical results, the pair of solutions given by the above Eq. (41) is classically unstable.…”

“…This is the pontential considered in [8], and here we use the same notation, with λ, f and d real and positive. In this case we see that…”

PT-symmetric kinks

“…In other words, the vacuum states act as implicit boundary conditions of the BPS equations. Now, instead of applying the usual trial-orbit approach [35][36][37][38][39][40][41], we note that it is possible to write the following equation:…”

Degenerate and critical Bloch branes

“…A couple of years ago one of us presented a method for finding additional soliton solutions for those special cases whose soliton solutions are the BPS ones [35] and in the last year that approach was extended, allowing more general models [36,37,41]. This last approach is the one we will use along this manuscript.…”