Related papers: The $\phi^4$ kink on a wormhole spacetime
We present a review of our recent works directed towards discovery of a periodic, kink-like and soliton-like travelling wave solutions within the models of transport phenomena and the mathematical biology. Analytical description of these…
Light-like galileon solutions have been used to investigate the chronology problem in galileon-like theories, and in some cases may also be considered as solitons, evading a non-existence constraint from a zero-mode argument. Their…
We consider the issue of stability at the linearized level for static, spherically symmetric wormhole solutions within a subclass of scalar-tensor theories of beyond Horndeski type. In this class of theories we derive a set of stability…
We discuss the properties of Lorentzian wormholes in dilatonic Einstein-Gauss-Bonnet theory in four spacetime dimensions. These wormholes do not need any form of exotic matter for their existence. A subset of these wormholes is shown to be…
We investigate the time evolution of spherically symmetric radial domain walls (kinks) in the background of a two-way traversable Simpson-Visser wormhole. By numerically solving the scalar-field equation with a double-well potential, we…
A stable soliton configuration for a nucleon emerges when the nucleon stability and $\Sigma_N$ term discrepancy problems are studied semi-quantitatively within a local theory developed recently. The approach developed here goes beyond the…
In the present work we discuss non-linear physics problems such as Nielsen-Olesen strings, superconducting bosonic straight strings and static vortex rings. We start with a toy model. We search for antiperiodic solitons of the Goldstone…
We determine the stability conditions for a radially symmetric noncommutative scalar soliton at finite noncommutivity parameter $\theta$. We find an intriguing relationship between the stability and existence conditions for all level-1…
Based on the recently introduced black-bounce spacetimes, we shall consider the construction of the related spherically symmetric thin-shell traversable wormholes within the context of standard general relativity. All of the really unusual…
We prove the orbital stability of soliton solutions for 2D Maxwell--Lorentz system with extended charged particle. The solitons corresponds to the uniform motion and rotation of the particle. We reduce the corresponding Hamilton system by…
We consider spherically symmetric configurations in general relativity, supported by nonlinear electromagnetic fields with gauge-invariant Lagrangians depending on the single invariant $f = F_{\mu\nu} F^{\mu\nu}$. Static black hole and…
Directed motion of topological solitons (kinks or antikinks) in the damped and AC-driven discrete sine-Gordon system is investigated. We show that if the driving field breaks certain time-space symmetries, the soliton can perform…
Linear stability analysis of the axisymmetric interface of velocity and density discontinuity in rotating gaseous disk has been performed numerically and analytically. Physical mechanisms leading to development of centrifugal and…
We construct a family of smooth charged bubbling solitons in $\mathbb{M}^4 \times$T$^2$, four-dimensional Minkowski with a two-torus. The solitons are characterized by a degeneration pattern of the torus along a line in $\mathbb{M}^4$…
We investigate four-dimensional gradient shrinking Ricci solitons with positive modified sectional curvature. Our first main result shows that if the norm of the self-dual Weyl tensor and the scalar curvature satisfy a certain sharp…
Single solitons are a special limit of more general waveforms commonly referred to as cnoidal waves or Turing rolls. We theoretically and computationally investigate the stability and accessibility of cnoidal waves in microresonators. We…
We give an exhaustive, non-perturbative classification of exact travelling-wave solutions of a perturbed sine-Gordon equation (on the real line or on the circle) which is used to describe the Josephson effect in the theory of…
In this work we consider a model where the potential has two topological sectors connecting three adjacent minima, as occurs with the $\phi^6$ model. In each topological sector, the potential is symmetric around the local maximum. For…
In this paper, we investigate how charge and modified terms affect the viability and stability of traversable wormhole geometry in the framework of $f(R,G)$ theory, where $R$ is the Ricci scalar and $G$ is the Gauss-Bonnet term. For this…
The static spherically symmetric thin shell of proper mass $m$ and electric charge $q$ around a central star or black hole of mass $M$ is in general unstable. Although with fine-tuned $m,q,$ and $M$ it can be considered quasi-stable. These…