Study of Stability of a Charged Topological Soliton in the System of Two Interacting Scalar Fields

Abstract

An analytical-numerical analysis of the singular self-adjoint spectral problem for a system of three linear ordinary second-order differential equations defined on the entire real exis is presented. This problem comes to existence in the nonlinear field theory. The dependence of the differential equations on the spectral parameter is nonlinear, which results in a quadratic operator Hermitian pencil.

Scattering of kinks of the sinh-deformed $φ^4$ model

“…In this more general context, several works have developed analytical solutions, which, in turn, has allowed one to study their stability and to use them in application of interest in physics [29][30][31][32][33][34][35][36][37][38][39][40]. Other investigations have dealt with the presence of junctions and/or intersections of defects [41][42][43][44], and with issues related to composite-kink internal structures, twinlike models with several fields and scalar triplet on domain walls [45][46][47][48][49][50][51][52][53][54][55][56][57], among other issues.…”

Transitions between topologically non-trivial configurations

“…Nevertheless, we will study onedimensional configurations. Thus the multi-field inflationary models are connected with (1 + 1)dimensional field-theoretical models, where many important results have been obtained recently, in particular, related to soliton interactions [11][12][13][14][15][16][17][18][19], soliton stability [20], bubble decay [21,22], and planar domain walls [23][24][25][26][27][28], see also book [9] and review [29].…”

Multi-kink scattering in the double sine-Gordon model

“…It is worth to mention that kink-like solutions can also be obtained in more complicated models with two or more scalar fields [37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53]. In particular, in [37,38,41,[47][48][49][50][51][52] the models with two real scalar fields with polynomial potentials have been studied.…”