Generation of soliton bubbles in a sine-Gordon system with localised inhomogeneities

Abstract

Nonlinear wave propagation plays a crucial role in the functioning of many physical and biophysical systems. In the propagation regime, disturbances due to the presence of local external perturbations, such as localised defects or boundary interphase walls have gained great attention. In this article, the complex phenomena that occur when sine-Gordon line solitons collide with localised inhomogeneities are investigated. By a one-dimensional theory, it is shown that internal modes of two-dimensional sine-Gordon solitons can be activated depending on the topological properties of the inhomogeneities. Shape mode instabilities cause the formation of bubble-like and drop-like structures for both stationary and travelling line solitons. It is shown that such structures are formed and stabilised by arrays of localised inhomogeneities distributed in space. Implications of the observed phenomena in physical and biological systems are discussed.

Bubble evolution around heterogeneities in ϕ4-field theories

“…In our system, solving an inverse problem, it is possible to give systems of type (2.8) with exact solutions. Later, in the sense of the qualitative theory of nonlinear dynamical systems [17], it is possible to generalise analytical results obtained for systems of type (2.8) to other solutions that are topologically equivalent [20,[37][38][39][40][41]. For instance, a natural generalisation of a kink in D + 1-dimensional systems with rotational symmetry is the following soliton-bubble…”

“…Shape modes are responsible for variations in the kink-like profile of the bubble wall and may affect the global dynamics of the bubble. A phenomenon termed as shape-mode instability occurs when a shape mode becomes unstable [20,[39][40][41]48]. In this scenario, the shape of the wall is no longer stable and the bubble breaks up.…”

Solitons and Instantons in Vacuum Stability: Physical Phenomena

“…First-order phase transition is one of the most important problems in condensed matter, particle physics, and cosmology [1][2][3][4][5][6][7][8][9][10]. This field has applications in vacuum stability [1], quark confinement [3], and cosmological models [11].…”

“…with Q > 0 and b > 0, where all the balls are outside the unstable equilibrium, do not lead to an evolution where the chain falling to the abyss.Figures 4,5,6,7,8,9,10,11,and 12 show the results from numerical simulations for different values of parameters φ 0 , Q, and b. The initial structure is unstable and collapses in time, giving a constant phase φ 0 throughout all space at long times.…”

Stability of bubble-like fluxons in disk-shaped Josephson junctions in the presence of a coaxial dipole current

“…In the two-dimensional case, the authors have recently reported the formation of a flux line closed in a loop with a radially-symmetric bubble-like structure: a bubble fluxon [34]. The dynamics and stability of topologically equivalent structures in Klein Gordon (KG) systems have gained significant attention in the literature, ranging from condensed matter to cosmology [4,[35][36][37][38][39][40][41][42][43]. Thus, theoretical studies on the formation, stability, and dynamics of bubble-like structures are relevant not only for heterogeneous sG systems but also for more general systems.…”