Search for long-living topological solutions of nonlinear ${\phi }^4$ field theory

Abstract

We look for long-living topological solutions of classical nonlinear $(1+1)-$ dimensional ${\phi }^4$ field theory. To that effect we use the well-known cut-and-match method. In this framework, new long-living states are obtained in both topological sectors. In particular, in one case a highly excited state of a kink is found. We discover several ways of energy reset. In addition to the expected emission wave packets (with small amplitude), for some selected initial conditions the production of kink-antikink pairs results in a large energy reset. Also, the topological number of a kink in the central region changes in the contrast of saving full topological number. At lower excitation energies there is a long-living excited vibrational state of the kink; this phenomenon is the final stage of all considered initial states. Over time this excited state of the kink changes to a well-known linearized solution - a discrete kink excitation mode. This method yields a qualitatively new way to describe the large-amplitude bion, which was detected earlier in the kink-scattering processes in the nontopological sector.

arXiv comment13 pages, 11 figures

References in corpus (10)

• Kink interactions in the (1+1)-dimensional ${\phi }^6$ model
• Kink-antikink interactions in the double sine-Gordon equation and the problem of resonance frequencies
• Domain Walls as Dark Energy
• Kink excitation spectra in the (1+1)-dimensional ${\phi }^8$ model
• Wobbling kinks in ${\varphi }^4$ theory
• Scalar triplet on a domain wall: an exact solution
• Fluctuation - induced nucleation and dynamics of the kinks on dislocation. Soliton and oscillation regimes in 2D Frenkel-Kontorova model
• Resonantly driven wobbling kinks
• Kink nucleation in two-dimensional Frenkel-Kontorova model
• Defect Structures in Field Theory

Cited by in corpus (2)

• Extreme values of elastic strain and energy in sine-Gordon multi-kink collisions
• An introduction to kinks in ${\phi }^4$-theory