Related papers: Notes on Periodic Solitons
For a class of $(N+1)$-dimensional systems of differential delay equations with a cyclic and monotone negative feedback structure, we construct a two-dimensional invariant manifold, on which phase curves spiral outward towards a bounding…
This paper presents a comprehensive analysis of several aspects of the sinh-Gordon equation within a periodic setting. Our investigation proceeds in three main stages. First we establish the existence of periodic solutions for a fixed wave…
We consider a dc-driven damped sine-Gordon model with a small nonlinear spatial-disorder term, onto which a sinusoidal modulation is superimposed. It describes, e.g., a weakly disordered system with a regular grain structure. We demonstrate…
We demonstrate that the commonly known concept, which treats solitons as nonsingular solutions produced by the interplay of nonlinear self-attraction and linear dispersion, may be extended to include modes with a relatively weak singularity…
We consider non-topological, "bell-shaped" localized and regular solutions available in some 1+1 dimensional scalar field theories. Several properties of such solutions are studied, namely their stability and the occurence of fermion bound…
We analyse several physical aspects of the dressed elliptic strings propagating on $\mathbb{R} \times \mathrm{S}^2$ and of their counterparts in the Pohlmeyer reduced theory, i.e. the sine-Gordon equation. The solutions are divided into two…
We construct and simulate the dynamics of gauged vortons - circular loops of cosmic string supported by the angular momentum of trapped charge and current and provide additional details on the fully stable vorton that we have previously…
We consider a particular truncation of the generalized Proca field theory in four dimensions for which we construct a static and axisymmetric rotating black hole "stealth solutions", namely solutions with (Anti) de Sitter or Kerr metric but…
The set of real finite-gap Sine-Gordon solutions corresponding to a fixed spectral curve consists of several connected components. A simple explicit description of these components obtained by the authors recently is used to study the…
In this work, kinks with non-canonical kinetic energy terms are studied in a type of two-dimensional dilaton gravity model. The linear stability issue is generally discussed for arbitrary static solutions, and the stability criteria are…
A generalization of Jacobi's elliptic functions is introduced as inversions of hyperelliptic integrals. We discuss the special properties of these functions, present addition theorems and give a list of indefinite integrals. As a physical…
We study the self-dual Chern-Simons Higgs theory on an asymptotically flat cylinder. A topological multivortex solution is constructed and the fast decaying property of solutions is proved
The sine-Gordon model with space- and time-dependent parameters is considered. A highly accurate effective model with two degrees of freedom is constructed, allowing the description of the kink movement in this model even for extremely long…
The scattering of kinks and low-frequency breathers of the nonlinear sine-Gordon (SG) equation on a spatially localized $\mathcal{PT}$-symmetric perturbation (defect) with a balanced gain and loss is investigated numerically. It is…
In recent researches of the dynamics of solitons, it is gradually revealed that oscillation modes play a crucial role when we analyze the dynamics of solitons. Some dynamical properties of solitons on external potentials are studied with…
We study the semiclassical Einstein field equations with a Klein-Gordon field in ultrastatic and static spacetimes. In both cases, the equations for the spacetime metric become constraint equations. In the ultrastatic case, the Hadamard…
We explicitly construct a large class of finite-volume two-magnon string solutions moving on R x S^2. In particular, by making use of the relationship between the O(3) sigma model and sine-Gordon theory we are able to find solutions…
We study the stability of standing-waves solutions to a scalar non-linear Klein-Gordon equation in dimension one with a quadratic-cubic non-linearity. Orbits are obtained by applying the semigroup generated by the negative complex unit…
We consider the Sine-Gordon model coupled to 2D gravity. We find a nonperturbative expression for the partition function as a function of the cosmological constant, the SG mass and the SG coupling constant. At genus zero, the partition…
We investigate the dynamics of the sine-Gordon solitons perturbed by spatiotemporal external forces. We prove the existence of internal (shape) modes of sine-Gordon solitons when they are in the presence of inhomogeneous space-dependent…