相关论文: General solution of overdamped Josephson junction …

This paper is focused on the generalized Forchheimer flows of isentropic gas, described by a system of two nonlinear degenerating differential equations of first order. We prove the existence and uniqueness of the Dirichlet problem for…

Various types of the current-phase relation I(phi) in superconductor-ferromagnet-superconductor (SFS) point contacts and planar double-barrier junctions are studied within the quasiclassical theory in the limit of thin diffusive…

In this paper, the existence and number of non-contractible limit cycles of the Josephson equation $\beta \frac{d^{2}\Phi}{dt^{2}}+(1+\gamma \cos \Phi)\frac{d\Phi}{dt}+\sin \Phi=\alpha$ are studied, where $\phi\in \mathbb S^{1}$ and…

The overdamped Josephson junction in superconductivity theory can be modeled by the family of dynamical systems on the torus, which is known as the RSJ model. This family admits an equivalent description by a family of second-order…

We prove a necessary and sufficient condition for the existence of a $T$-periodic solution for the time-periodic second order differential equation $\ddot{x}+f(t,x)+p(t,x,\dot x)=0$, where $f$ grows superlinearly in $x$ uniformly in time,…

We obtain several higher order exact periodic solutions of (i) a coupled symmetric phi4 model in an external field, (ii) an asymmetric coupled phi4 model, (iii) an asymmetric-symmetric coupled phi4 model, in terms of Lame polynomials of…

We present new necessary and sufficient conditions for the existence of fixed points in a finite system of coupled phase oscillators on a complete graph. We use these conditions to derive bounds on the critical coupling.

We investigate a system of two- and three-body constrained dipolar bosons in a pair of one-dimensional optical lattices coupled to each other by the non-local dipole-dipole interactions. Assuming attractive dipole-dipole interactions, we…

In this paper, we analyze the solutions of the following non-linear differential-difference equations f^n(z) +\omega f^(n-1)f'(z) +p(z)f(z+c) = p_1e^{\alpha}_1z +p_2e^{\alpha}_2z and f^n(z)f'(z) +q(z)e^Q(z)f(z+c) = p_1e^{\alpha}_1z…

In this short note, we review several one-dimensional problems such as those involving linear Schroedinger equation, variable-coefficient Helmholtz equation, Zakharov-Shabat system and Kubelka-Munk equations. We show that they all can be…

An array of resistively and capacitively shunted Josephson junctions with nonsinusoidal current-phase relation is considered for modelling the transition in high-T$_c$ superconductors. The emergence of higher harmonics, besides the simple…

We have designed an experiment and performed extensive simulations and preliminary measurements to identify a set of realistic circuit parameters that should allow the observation of constant-current steps at I=2ef in short arrays of small…

Classical conditions for asymptotic stability of periodic solutions bifurcating from a limit cycle rely on the derivative of the corresponding bifurcation function F at the bifurcation point t. We show that for analytic systems this result…

This article gives a ``fundamental solution'' based energy-norm harmonic interpolation approach for two half-space settings of interest: the upper-half $\mathbb{R}^n$ plane, where fundamental solutions satisfy Laplace's equation, and the…

We consider a class of nonlinear Fokker-Planck equations describing the dynamics of an infinite population of units within mean-field interaction. Relying on a slow-fast viewpoint and on the theory of approximately invariant manifolds we…

We consider a two-component linearly-coupled system with the intrinsic cubic nonlinearity and the harmonic-oscillator (HO) confining potential. The system models binary settings in BEC and optics. In the symmetric system, with the HO trap…

In this paper we present sufficient conditions for the existence of heteroclinic or homoclinic solutions for second order coupled systems of differential equations on the real line. We point out that it is required only conditions on the…

The problem of vortex structure in a single Josephson junction in an external magnetic field, in the absence of transport currents, is reconsidered from a new mathematical point of view. In particular, we derive a complete set of exact…

We consider phase-locked dynamics of a Josephson junction driven by finite-spectral-linewidth ac current. By means of a transformation, the effect of frequency fluctuations is reduced to an effective additive noise, the corresponding…

We present an experimental realization of the Optical Frequency Locked Loop (OFLL) applied to long-term frequency difference stabilization of broad-line DFB lasers. The presented design, based on an integrated phase-frequency detector chip,…