The affective factors on the uncertainty in the collisions of the soliton solutions of the double field sine-Gordon system

Abstract

Inspired by the well known sine-Gordon equation, we present a symmetric coupled system of two real scalar fields in 1 + 1 dimensions. There are three different topological soliton solutions which be labelled according to their topological charges. These solitons can absorb some localized non-dispersive wave packets in collision processes. It will be shown numerically, during collisions between solitons, there will be an uncertainty which originates from the amount of the maximum amplitude and arbitrary initial phases of the trapped wave packets. * physmohammadi@pgu.ac.ir † n˙riazi@sbu.ac.ir 1 arXiv:1906.07498v1 [nlin.PS]

Kink-Antikink Collisions in the Periodic $φ^{4}$ Model

“…For example, for the φ 4 (periodic ϕ 4 ) system, which was introduced in the pervious section, the related kink potential is U(x) = 4 − 6 sech 2 (x) for which there is a non-trivial bound state (internal mode) corresponding to ω 2 o = 3 and ψ ∝ tanh(x) sech(x) [26,67]. The other systems, which have no non-trivial bound states, can never maintain a constantly oscillating behaviour after the collisions [22,27,70]. In fact, any non-trivial internal mode can be considered as a channel to impose an additional fluctuation on the kink (antikink) solution.…”

“…Especially in cosmology, the structure and dynamics of domain walls, can be modeled or described by the (1+1)-dimensional kink-bearing theories [9][10][11][12][13][14]. Topological kink (-like) solutions also exist in more complex models with two or more fields in (1 + 1)-dimensions [15][16][17][18][19][20][21][22][23]. Complex kink (anti-kink) solution is another type of topological soliton-like solutions which was obtained for a complex nonlinear Klein-Gordon field system [24].…”

Scattering of the asymmetric $ϕ^6$ kinks from a $\mathcal{PT}$-symmetric perturbation: Creation of multiple pairs of kink-antikink from phonons

“…For that reason kinks interaction in higher order models is more interesting and some phenomenons like resonant scattering structure, escape windows [47][48][49] or even the extreme values of the energy densities [50] depend on the order in which kinks collide. Many important results have also been obtained for topological field configurations in [51][52][53][54][55][56][57][58][59][60][61][62][63][64][65]. Consequently, it is important to know how an asymmetric φ 6 kink treats when it interacts with a PT -symmetric perturbation.…”

Collision, mechanism, and $Z_4$ operation among chiral and nonchiral kinks in coupled double-field $ϕ^4$ model

“…These exotic features are attributed to the excitation of internal modes and explained by the resonant energy exchange between translational (or zero) and vibrational modes. Furthermore, kinks and their dynamics have been studied in various nonintegrable single-field models [17][18][19][20][21][22][23][24][25][26][27][28][29] and multifield models [30][31][32][33][34][35][36][37][38][39][40][41]. In particular, the multifield models show complex and plentiful kink dynamics due to the additional degree of freedom.…”