Related papers: Resonant normal form for even periodic FPU chains
Let $\Phi'$ denote the strong dual of a nuclear space $\Phi$. In this paper we introduce sufficient conditions for the convergence uniform on compacts in probability for a sequence of $\Phi'$-valued processes with continuous or…
Topological phases supporting non-abelian anyonic excitations have been proposed as candidates for topological quantum computation. In this paper, we study disordered non-abelian anyonic chains based on the quantum groups $SU(2)_k$, a…
We propose the algorithm for determining vibrational quantum eigenstates of periodic linear chain of atoms coupled by harmonic and third order anharmonic interactions (Fermi-Ulam-Pasta $\alpha$ problem) in the long wavelength limit within…
We have considered the following semi linear elliptic problem on the unit disk $B$ $-\Delta u = \lambda_1 u+e^u+f $ in $B$ with the Dirichlet boundary condition and $f$ satisfying the following condition : $f\in L^r(B)$, for some $r>2$ and…
We study periodic solutions for a quasi-linear system, which is the so called dispersionless Lax reduction of the Benney moments chain. This question naturally arises in search of integrable Hamiltonian systems of the form $ H=p^2/2+u(q,t)…
For piecewise monotone interval maps we look at Birkhoff spectra for regular potential functions. This means considering the Hausdorff dimension of the set of points for which the Birkhoff average of the potential takes a fixed value. In…
We report on the realization of a Fermi-Fermi mixture of ultracold atoms that combines mass imbalance, tunability, and collisional stability. In an optically trapped sample of $^{161}$Dy and $^{40}$K, we identify a broad Feshbach resonance…
It has recently been pointed out that Fermi surfaces can remain even in the superconductors under the symmetric spin-orbit interaction and broken time-reversal symmetry. Using the linear response theory, we study the instability of such…
In this paper, we study the properties of the Fermat-Weber point for a set of fixed points, whose arrangement coincides with the vertices of a regular polygonal chain. A $k$-chain of a regular $n$-gon is the segment of the boundary of the…
We present an analytic theory unraveling the microscopic mechanism of instabilities within interacting $D$-dimensional Fermi liquid. Our model consists of a $D$-dimensional electron gas subject to an instantaneous electron-electron…
In this paper we study a non-linear partial differential equation (PDE), proposed by N. Kudryashov [arXiv:1611.06813v1[nlin.SI]], using continuum limit approximation of mixed Fermi-Pasta-Ulam and Frenkel-Kontorova Models. This generalized…
This paper investigates the regularity of stable radial solutions to semilinear elliptic equations arising in MEMS problems, modeled by the Dirichlet problem $-\Delta u=f(u)$ in the unit ball $B_1$, where the nonlinearity $f\in C^1([0,1))$…
In this paper, we consider the normal form problem of a commutative family of germs of diffeomorphisms at a fixed point, say the origin, of $\mathbb{K}^n$ ($\mathbb{K}=\mathbb{C}$ or $\mathbb{R}$). We define a notion of integrability of…
Every orthonomic system of partial differential equations is known to possess a finite number of integrability conditions sufficient to ensure the validity of all. Herewith we offer an efficient algorithm to construct a sufficient set of…
Recent achievements in experiments with cold fermionic atoms indicate the potential for developing novel superconducting devices which may be operated in a wide range of regimes, at a level of precision previously not available. Unlike…
We are mainly concerned with equations of the form $-Lu=f(x,u)+\mu$, where $L$ is an operator associated with a quasi-regular possibly nonsymmetric Dirichlet form, $f$ satisfies the monotonicity condition and mild integrability conditions,…
We prove that the Ziegler pendulum -- a double pendulum with a follower force -- can be integrable, provided that the stiffness of the elastic spring located at the pivot point of the pendulum is zero and there is no friction in the system.…
We study the integrability of the Hamiltonian normal form of 1 : 2 : 2 resonance. It is known that this normal form truncated to order three is integrable. The truncated to order four normal form contains too many parameters. For a generic…
Let $\Phi$ be a nuclear space and let $\Phi'$ denote its strong dual. In this paper we introduce sufficient conditions for the almost surely uniform convergence on bounded intervals of time for a sequence of $\Phi'$-valued processes having…
In this paper, we prove a phase transition in the connectivity of Finitary Random interlacements $\mathcal{FI}^{u,T}$ in $\mathbb{Z}^d$, with respect to the average stopping time. For each $u>0$, with probability one $\mathcal{FI}^{u,T}$…