相关论文: General solution of overdamped Josephson junction …
We consider the fully nonlinear equation with variable-exponent double phase type degeneracies $$ \big[|Du|^{p(x)}+a(x)|Du|^{q(x)}\big]F(D^2u)=f(x). $$ Under some appropriate assumptions, by making use of geometric tangential methods and…
\noindent Using the techniques connected with the measure of noncompactness we investigate the neutral difference equation of the following form \begin{equation*} \Delta \left(r_{n}\left(\Delta \left(x_{n}+p_{n}x_{n-k}\right) \right)…
The dynamics of a one-degree of freedom oscillator with arbitrary polynomial non-linearity subjected to an external periodic excitation is studied. The sequences (cascades) of harmonic and subharmonic stationary solutions to the equation of…
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…
We present an exact mathematical description of the Meissner effect and of the vortex state in periodic thin-layer superconductor/insulator structures with an arbitrary number of identical junctions N-1 (N is the number of superconducting…
In this paper, two numerical approaches based on the Newton iteration method with spectral algorithms are introduced to solve the Thomas-Fermi equation. That Thomas-Fermi equation is a nonlinear singular ordinary differential equation (ODE)…
In this work, we give the power series solutions around an ordinary point, in the case of variable coefficients, homogeneous sequential linear conformable fractional differential equations of order 2\alpha. Further, we introduce the…
We investigate a coupled system of elliptic equations of Lane--Emden--Fowler type on a bounded domain $\Omega \subset \mathbb{R}^n$ ($n \geq 1$) with homogeneous Dirichlet boundary conditions. The system is characterized by sublinear…
For first order differential equations of the form $y'=\sum_{p=0}^P F_p(x)y^p$ and second order homogeneous linear differential equations $y''+a(x)y'+b(x)y=0$ with locally integrable coefficients having asymptotic (possibly divergent) power…
In this work, we study the generalization of decohered average symmetry-protected topological phases to open quantum systems with a combination of subsystem symmetries and global symmetries. In particular, we provide examples of two types…
In a very interesting recent Letter\cite{machida}, the authors suggested the possibility of realizing the spatially modulated, or Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid state in trapped atomic fermion systems. The authors this…
In this article a two-sided variable coefficient fractional diffusion equation (FDE) is investigated, where the variable coefficient occurs outside of the fractional integral operator. Under a suitable transformation the variable…
A sharp condition is provided to guarantee that the (nontrivial) solutions of a DDE of the form $\dot{x}(t)+F(t,x)=0$ $t\geq 0,$ (where $F(t,\cdot)$ is an odd-like causal operator) either oscillate, or converge monotonically to zero. The…
A periodic two-phase algebro-geometric solution of the focusing nonlinear Schr\"odinger equation is constructed in terms of elliptic Jacobi theta-functions. A dependence of this solution on the parameters of a spectral curve is…
The ground state of the $\SO(2n)_{1} \times \SO(2n)_{1} \over \SO(2n)_{2}$ coset theories, perturbed by the $\phi^{id,id}_{adj}$ operator and those of the sine-Gordon theory, for special values of the coupling constant in the attracting…
A novel method is developed for constructing periodic solutions of a model equation describing nonlocal Josephson electrodynamics. This method consists of reducing the equation to a system of linear ordinary differential equations through a…
For a singularly perturbed system of reaction--diffusion equations, assuming that the 0th order solutions in regular and singular regions are all stable, we construct matched asymptotic expansions for formal solutions to any desired order…
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have…
We propose a regularization of the BFKL equation which allows for its solution in each order of perturbation theory by means of a sum over multiple poles. This sum can be presented in a rather simple formula for the Fourier transform in the…
We demonstrate experimentally the existence of Josephson junctions having a doubly degenerate ground state with an average Josephson phase \psi=\pm{\phi}. The value of {\phi} can be chosen by design in the interval 0<{\phi}<\pi. The…