Abstract
A systematic procedure for obtaining defect structures through cyclic deformation chains is introduced and explored in detail. The procedure outlines a set of rules for analytically constructing constraint equations that involve the finite localized energy of cyclically generated defects. The idea of obtaining cyclically deformed defects concerns the possibility of regenerating a primitive (departing) defect structure through successive, unidirectional, and eventually irreversible, deformation processes. Our technique is applied on kink-like and lump-like solutions in models described by a single real scalar field such that extensions to quantum mechanics follow the usual theory of deformed defects. The preliminary results show that the cyclic device supports simultaneously kink-like and lump-like defects into 3- and 4-cyclic deformation chains with topological mass values closed by trigonometric and hyperbolic deformations. In a straightforward generalization, results concerning the analytical calculation ofN-cyclic deformations are obtained, and lessons regarding extensions from more elaborated primitive defects are depicted.
Highlights
Solutions of a restricted class of nonlinear equations yield an ample variety of topological and nontopological defects of current interest, in particular to mathematical and physical applications as well [1, 2]
We have introduced and scrutinized a systematic procedure for obtaining defect structures through cyclic deformation chains involving topological and nontopological solutions in models described by a single real scalar field
After embedding some previously investigated deformed defect structures, namely, the Sine-Gordon kink, and the bellshaped lump-like structure, into a 3-cyclic deformation chain supported by the primitive kink solution of the λφ4 theory, we have investigated the existence of a systematic technique to obtain novel defect structures
Summary
Solutions of a restricted class of nonlinear equations yield an ample variety of topological (kink-like) and nontopological (lump-like) defects of current interest, in particular to mathematical and physical applications as well [1, 2]. Our work is concerned with a systematic procedure for defect generation defined through trigonometric and hyperbolic bijective deformation functions They allow the construction of N-finite cyclic deformation chains involving topological and nontopological solutions. The main issues that have stimulated us to investigate cyclically deformed defects have appeared through the BPS first-order framework [32, 34, 35] for obtaining kink-like and lump-like structures Such an outstanding process of systematically obtaining cyclically deformed defects allows reedifying a preliminarily introduced defect structure—for instance, the usual kink defect from the λφ theory—through successive, unidirectional, and eventually irreversible, deformation operations. This possibility of regenerating a primitive defect is one of our principal concerns in this work.
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