Scattering of sine-Gordon kinks with internal structure in an extended nonlinear O(3) sigma model

Abstract

Abstract In this paper, we present topological defects in (1, 1) dimensions, described by an extended nonlinear O(3) sigma model. We consider spherical coordinates (ϕ, χ) in the isotopic space S 2 and a potential V (ϕ, χ). For specific forms of the potential, the Bogomolnyi method is applicable, yielding first-order equations of motion with solutions that minimize energy. We study a model with an explicit solution for the field ϕ that resembles the ubiquitous sine-Gordon kink/antikink but with an internal structure given by the field χ with a form antilump/lump that depends on a constant C. The soliton-antisoliton scattering process depends on C and on the initial velocity of the pair. Some results are reported, such as: one-bounce scattering for ϕ, or strong radiation emission for ϕ, followed by i) annihilation of χ; ii) same pattern antilump-antilump or lump-antilump for χ; iii) inversion antilump-antilump to lump-lump for χ; iv) inversion antilump-lump to lump-antilump for χ. Other findings are: v) annihilation of the soliton-antisoliton pair with the emission of scalar radiation; vi) emission of a pair of oscillating pulses around the vacuum. The energy density indicates that the defect possesses an internal structure, specifically as a nested defect of an antilump within a kink. The lump core of the defect is responsible for emitting radiation. The change in the structure of the defects during scattering is analyzed not only in terms of field profiles in the physical (1, 1) space but also in the internal S 2 space, which provides new insight into the process.

Keywords

• Field Theories in Lower Dimensions
• Sigma Models
• Solitons Monopoles and Instantons