Bubblelike structures generated by activation of internal shape modes in two-dimensional sine-Gordon line solitons

Abstract

Nonlinear waves that collide with localized defects exhibit complex behavior. Apart from reflection, transmission, and annihilation of an incident wave, a local inhomogeneity can activate internal modes of solitons, producing many impressive phenomena. In this work we investigate a two-dimensional sine-Gordon model perturbed by a family of localized forces. We observed the formation of bubblelike and droplike structures due to local internal shape mode instabilities. We describe the formation of such structures on the basis of a one-dimensional theory of activation of internal modes of sine-Gordon solitons. An interpretation of the observed phenomena, in the context of phase transition theory, is given. Implications in Josephson junctions with a current dipole device are discussed.

Scattering of the φ8 kinks with power-law asymptotics

“…Today, the study of the properties of topological defects is a vast and very fast developing area. Interactions of kinks with each other and with impurities have been studied [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]; see also results for branes [44], bubble-like structures [45,46], interactions of breathers [47], and so on [48][49][50][51][52][53][54]. Many interesting and important results have been obtained in the (1+1)dimensional models with polynomial potentials: ϕ 4 , ϕ 6 , ϕ 8 , and so on [55][56][57][58][59][60][61][63][64][65][66][67][68][69][70]].…”

Exact Topological Soliton Solutions to the Strongly Perturbed Family of Sine-Gordon Type Equations

“…Substituting (9) into (8) and setting the coefficients to the linearly independent functions both to zero gives us the first solution to the unperturbed DSGE. The details of this process are given in Appendix B.…”

“…Again, the details of this process are given in Appendix B. Here, we will use the first Ansatz, (9). Solving as before leads to the first solution to the perturbed DSGE.…”

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.…”