Related papers: A remark on rational isochronous potentials

We prove the existence of a ground state positive solution of Schr\"odinger-Poisson systems in the plane of the form $$ -\Delta u + V(x)u + \frac{\gamma}{2\pi} \left(\log|\cdot| \ast u^2 \right)u = b |u|^{p-2}u \qquad\text{in}\…

The basic aim is to extend some results and concepts of non-autonomous second order differential systems with convex potentials to the new context of multi-time Poisson-gradient PDE systems with convex potential. In this sense, we prove…

A homogenization result for a family of integral energies is presented, where the fields are subjected to periodic first order oscillating differential constraints in divergence form. The work is based on the theory of A -quasiconvexity…

We consider the rationally extended harmonic oscillator potential which is isospectral to the conventional one and whose solutions are associated with the exceptional, $X_m$- Hermite polynomials and discuss its various important properties…

The integrable time-dependent central potentials that admit linear and quadratic first integrals other than those constructed from the angular momentum are determined. It is shown explicitly that previous answers to this problem are…

Using the techniques of equivariant bifurcation theory we prove the existence of non-stationary periodic solutions of $\Gamma$-symmetric systems $\ddot q(t)=-\nabla U(q(t))$ in any neighborhood of an isolated orbit of minima $\Gamma(q_0)$…

Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which…

Diffusion of electrons in a two-dimensional system with time-dependent random potentials is investigated numerically. The correction to the conductivity due to inelastic scatterings by oscillating potentials is shown to be a universal…

We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent…

We analyse the exact solutions of a conditionally-solvable Schr\"odinger equation with a rational potential. From the nodes of the exact eigenfunctions we derive a connection between the otherwise isolated exact eigenvalues and the actual…

The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical mechanical system is integrable with invariants that are…

We consider existence and stability of an almost periodic solution of the quasilinear system of differential equations with piecewise constant argument of generalized type. The associated linear homogeneous system satisfies exponential…

We show how the recently discovered solvable rational extensions of Harmonic Oscillator and Morse potentials can be constructed in a direct and systematic way, without the need of supersymmetry, shape invariance, Darboux-Crum and…

It is shown that for a central potential that is an injective function of the radial coordinate, a second central potential can be found that leads to trajectories in the configuration space and the momentum space coinciding, respectively,…

We consider two dimensional real-valued analytic potentials for the Schr\"odinger equation which are periodic over a lattice $L$. Under certain assumptions on the form of the potential and the lattice $L$, we can show there is a large class…

We consider here the coexistence of first- and third-order integrals of motion in two dimensional classical and quantum mechanics. We find explicitly all potentials that admit such integrals, and all their integrals. Quantum superintegrable…

We consider a continuum model of electrical signals in the human cortex, which takes the form of a system of semilinear, hyperbolic partial differential equations for the inhibitory and excitatory membrane potentials and the synaptic…

We discuss a systematic way in which a relational dynamics can be established relative to periodic clocks both in the classical and quantum theories, emphasising the parallels between them. We show that: (1) classical and quantum relational…

We establish the eventual periodicity of the spectrum of any monadic second-order formula where: (i) all relation symbols, except equality, are unary, and (ii) there is only one function symbol and that symbol is unary.

Different modern phase shift equivalent NN potentials are tested by evaluating the partial wave decomposition of the kinetic and potential energy of the deuteron. Significant differences are found, which are traced back to the matrix…