Related papers: $\pi$-kinks in strongly ac driven sine-Gordon syst…
Fluxon dynamics in the dc-biased array of asymmetric three-junction superconducting quantum interference devices (SQUIDs) is investigated. The array of SQUIDs is described by the discrete double sine-Gordon equation. It appears that this…
We address the issue of internal modes of a kink of a discrete sine-Gordon equation. The main point of the present study is to elucidate how the antisymmetric internal mode frequency dependence enters the quasicontinuum spectrum of…
In this work we study a model of interaction of kinks of the sine-Gordon equation with a weak defect. We obtain rigorous results concerning the so-called critical velocity derived in [7] by a geometric approach. More specifically, we prove…
The late time behavior of the slow-roll parameter in the stringy quintessence model is studied when axion as well as saxion are allowed to move. Even though the potential is independent of the axion at tree level, the axion can move through…
In this paper we construct a family of Hamilton-Jacobi separable non-linear $\mathbb{S}^1\times\mathbb{S}^1$ Sigma models for which the kink variety can be analytically identified and for which the linear stability of the emerging kinks is…
A stability criterion is derived for self-similar solutions with perfect fluids which obey the equation of state $P=k\rho$ in general relativity. A wide class of self-similar solutions turn out to be unstable against the so-called kink…
Recently for the sine-Gordon equation it has been established that during collisions of $N$ slow kinks maximal energy density increases as $N^2$. In this numerical study, the same scaling rule is established for the non-integrable $\phi^4$…
In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink…
We find a rich variety of counterintuitive features in the steady states of a qubit array coupled to a dissipative source and sink at two arbitrary sites, using a master equation approach. We show there are setups where increasing the pump…
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 show how to induce pairing of Cooper pairs (and, thus, $4e$ superconductivity) as a result of local embedding of a quantum impurity in a Josephson network fabricable with conventional junctions. We find that a boundary double Sine-Gordon…
A chain of interacting particles subject also to a nonlinear on-site potential admits stable soliton-like configurations : static kinks. The linear normal-modes around such a kink contain a discrete set of localized, gap-separated modes.…
We give a sufficient condition, in the spirit of Kowalczyk-Martel-Munoz-Van Den Bosch \cite{KMMvdB21AnnPDE}, for the local asymptotic stability of kinks under odd perturbations. In particular, we allow the existence of quite general…
We study the classical dynamics of an axion field (the signal) that is coupling into a Josephson junction (the detector) by means of a capacitive coupling of arbitrary size. Depending on the size of the coupling constant and the initial…
We consider discrete sine-Gordon equation on branched domains. The latter is modeled in terms of the metric graphs with discrete bonds having the form of the branched 1D chains. Exact analytical solutions of the problem are obtained for…
We investigate analytically long Josephson junctions with phase pi-discontinuity points. Such junctions are usually fabricated as a ramp between a superconductor like YBCO with d-wave symmetry of the order parameter and an s-wave…
We present a non-equilibrium quasiclassical formalism suitable for studying linear response ac properties of Josephson junctions. The non-equilibrium self-consistency equations are satisfied, to very good accuracy, already in zeroth…
We prove that semiclassical gravity in conformally static, globally hyperbolic spacetimes with a massless, conformally coupled Klein-Gordon field is well posed, when viewed as a coupled theory for the dynamical conformal factor of the…
We consider the stationary sine-Gordon equation on metric graphs with simple topologies. The vertex boundary conditions are provided by flux conservation and matching of derivatives at the star graph vertex. Exact analytical solutions are…
A controllable $\pi$-SQUID is a DC SQUID with two controllable $\pi$-junctions as weak links. A controllable $\pi$-junction consists of a superconducting - normal metal - superconducting Josephson junction with two additional contacts to…