Related papers: BPS solitons with internal structure in the gauged…
We generalize a recently developed ADHMN-like construction of self-dual string solitons using loop space. In particular, we present two extensions: The first one starts from solutions to the Basu-Harvey equation for the ABJM model, the…
We investigate a model for a real scalar field in bidimensional space-time, described in terms of a positive semi-definite potential that presents no vacuum state. The system presents topological solutions of the BPS type, with energy…
We study a d=2+1 dimensional Chern-Simons gauge theory coupled to a Higgs scalar and an axion field, finding the form of the potential that allows the existence of selfdual equations and the corresponding Bogomolny bound for the energy of…
Three dimensional (3D) relativistic electromagnetic sub-cycle solitons were observed in 3D Particle-in-Cell simulations of an intense short laser pulse propagation in an underdense plasma. Their structure resembles that of an oscillating…
We study how non-invertible self-duality defects arise in theories with a holographic dual. We focus on the paradigmatic example of $\mathfrak{su}(N)$ $\mathcal{N} = 4$ SYM. The theory is known to have non-invertible duality and triality…
The concept of soliton complex in a nonlinear dispersive medium is proposed. It is shown that strongly interacting identical topological solitons in the medium can form bound soliton complexes which move without radiation. This phenomenon…
The existence of stable solitons in two- and three-dimensional (2D and 3D) media governed by the self-focusing cubic nonlinear Schr\"{o}dinger equation with a periodic potential is demonstrated by means of the variational approximation (VA)…
We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell's term and subject to a so-called Gausson's self-dual potential. To carry out this study,…
We investigate the soliton structure of novel (2+1)-dimensional nonlinear partial differential evolution(NLPDE) equations which may govern the behavior of a barothropic relaxing medium beneath high-frequency perturbations. As a result, we…
We study non-linear electrodynamics in curved space from the viewpoint of dualities. After establishing the existence of a topological bound for self-dual configurations of Born-Infeld field in curved space, we check that the…
We study 1/4 Bogomol'nyi-Prasad-Sommerfield (BPS) composite solitons of vortex strings, domain walls and boojums in ${\cal N}=2$ supersymmetric Abelian gauge theories in four dimensions. We obtain solutions to the 1/4 BPS equations with the…
The connection between the supersymmetric quantum mechanics involving two-component eigenfunctions and the stability equation associated with two classical configurations is investigated, and a matrix superpotential is deduced. The issue of…
We systematically classify all possible Bogomol'nyi-Prasad-Sommerfield (BPS) equations in Euclidean dimension $d\leq8$. We discuss symmetries of BPS equations and their connection with the self-dual Yang-Mills equations. Also, we present a…
We investigate a generalized non-linear O(3) $\sigma$-model in three space dimensions where the fields are maps $S^3 \mapsto S^2$. Such maps are classified by a homotopy invariant called the Hopf number which takes integer values. The model…
The BPS Skyrme model is a model containing an $SU(2)$-valued scalar field, in which a Bogomol'nyi-type inequality can be satisfied by soliton solutions. In this model, the energy density of static configurations is the sum of the square of…
We perform the dimensional reduction of the nonrelativistic CP(1) model coupled to an Abelian Chern-Simons gauge field in the self-dual limit, and investigate the soliton and domain wall solutions of the emerging 1+1 dimensional self-dual…
Interaction of Double sine-Gordon solitons with a space dependent potential wall and also a potential well has been investigated by employing an analytical model based on the collective coordinate approach. The potential has been added to…
The Lee-Weinberg $U(1)$ magnetic monopoles, which have been reinterpreted as topological solitons of a certain non-Abelian gauged Higgs model recently, are considered for some specific choice of Higgs couplings. The model under…
We investigate a peculiar supersymmetry of the pairs of reflectionless quantum mechanical systems described by n-soliton potentials of a general form that depends on n scaling and n translation parameters. We show that if all the discrete…
We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave…