New results for deformed defects

Abstract

We extend a deformation prescription recently introduced and present some new soluble nonlinear problems for kinks and lumps. In particular, we show how to generate models which present the basic ingredients needed to give rise to dimension bubbles. Also, we show how to deform models which possess lumplike solutions, to get to new models that support kinklike solutions.

Kink interactions in the(1+1)-dimensionalφ6model

“…On the other hand, the case of (1+1) dimensions can be more easily investigated, hence the use of (1+1)-dimensional systems as simplified models. Note that it is an actively developing area, with many important results obtained recently: the topological defect deformation procedure [4,5], the construction of a topological defect carrying U(1) charge in a system with two scalar fields -one real and one complex [6,7], Q balls in scalar theories with U(1) symmetry [8,9], and many others. There are interesting results in scalar systems with an interaction with a spinor field [10][11][12].…”

Classical behavior of deformed sine-Gordon models

“…Then, considering non-bijective deformations [43], with f −1 being a multivalued function, we show how to deform a non-topological (lump-like) defect into a kink-like (topological) one. Functions f , for which the equation f ′ (φ) = 0 has finite solutions, can be also considered if the starting potential is such that V (χ) does not possess singularities.…”

“…[42] and extended in Refs. [43,44,45], consists in the following general prescription. Denote the deformed field by χ and assume that it is mapped into the starting field through the deformation function f , that is,…”

“…II, where we review some basic facts on the deformation procedure first introduced in [42] and further explored in Refs. [43,44,45,46,47,48,49]. In Sec.…”

Orbit-based deformation procedure for two-field models

“…Later, this method was adapted [9] for the searching of BPS states of systems of first order ODEs, leading to some advances. In recent years, other general methods for the investigation of complicated nonlinear problems arising in many-field systems which comprise multidefect solutions have been developed; see, for instance, [10,11,12,13,14,15] and references therein. Models of two scalar fields have also been used to describe complex phenomena such as the entrapment of topological defects; see, for instance [16,17,18].…”