Related papers: Scaling Identities for Solitons beyond Derrick's T…
We show how the famous soliton solution of the classical sine-Gordon field theory in $(1+1)$-dimensions may be obtained as a particular case of a solution expressed in terms of the Jacobi amplitude, which is the inverse function of the…
We derive a continuous family of virial identities for O($n$) symmetric configurations, parameterized by an exponent $\alpha$ that controls the radial weighting. The family provides a systematic decomposition of the global constraint into…
Subject of this talk is an overview of results on self-gravitating solitons of the classical Yang-Mills-Higgs theory. One finds essentially two classes of solitons, one of them corresponding to the magnetic monopoles the other one to the…
Tensor polynomial identities generalize the concept of polynomial identities on $d \times d$ matrices to identities on tensor product spaces. Here we completely characterize a certain class of tensor polynomial identities in terms of their…
This contribution reviews scalar-tensor theories whose Lagrangian contains second-order derivatives of a scalar field but nevertheless propagate only one scalar mode (in addition to the usual two tensor modes), and are thus not plagued with…
We obtain numerical solutions for rotating topological solitons of the nonlinear $\sigma$-model in three-dimensional Anti-de Sitter space. Two types of solutions, $i)$ and $ii)$, are found. The $\sigma$-model fields are everywhere well…
A number of identities are proved by using Stirling transforms. These identities involve Stirling numbers of the first and second kinds, hyperharmonic and derangement numbers, Bernoulli and Euler numbers and polynomials, powers, power sums,…
We uncover that, in contrast to the common belief, stable dissipative solitons exist in media with uniform gain in the presence of nonuniform cubic losses, whose local strength grows with coordinate x (in one dimension) faster than |x|. The…
If an outer (multilinear) commutator identity holds in a large subgroup of a group, then it holds also in a large characteristic subgroup. Similar assertions are valid for algebras and their ideals or subspaces. Varying the meaning of the…
The purpose of this paper is to propose a revised continuum model from the discrete system introduced in [Deng et.al., PRL, 2017] . Using a Galilean transformation, we obtain an equation governing the soliton solutions in the phase plane -…
Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially…
Finite-energy topological spherically symmetrical solutions of Chiral Born-Infeld Theory are studied. Properties of these solution are obtained, and a possible physical interpretation is also given.
We reconsider the detailed structure of the topological character of the instantons in pure Yang-Mills theory on $S^1\times\mathbb{R}^3$, so-called calorons. The claim is that the standard formula for the topological character, the second…
In this chapter we review recent results concerning localized and extended dissipative solutions of the discrete complex Ginzburg-Landau equation. In particular, we discuss discrete diffraction effects arising both from linear and nonlinear…
In view of the expectation that the solitonic sector of the lower dimensional world may be originated from the solitonic sector of string theory, various solitonic solutions are reduced from the heterotic fivebrane solutions in the…
Within the framework of the Inverse-Scattering formalism and the Hirota algorithm, soliton solutions of evolution equations are images of {\tau}-functions. Typically, the latter are expressed in terms of exponentials, the arguments of which…
In the continuum O(3) sigma model in two spatial dimensions, there are topological solitons whose size can be stabilized by adding Skyrme and potential terms. This paper describes a lattice version, namely a natural way of modifying the 2d…
We present a method to obtain soliton solutions to relativistic system of coupled scalar fields. This is done by examining the energy associated to static field configurations. In this case we derive a set of first-order differential…
We formulate a quantum coherent state picture for topological and non-topological solitons. We recognize that the topological charge arises from the infinite occupation number of zero momentum quanta flowing in one direction. Thus, the…
The presence of spinor fields is considered in the framework of some extensions of teleparallel gravity, where the Weitzenb\"ock connection is assumed. Some well known models as the Chaplygin gas and its generalizations are reconstructed in…