Related papers: The generalized MIC-Kepler system
Analytic-bilinear approach is used to study continuous and discrete non-isospectral symmetries of the generalized KP hierarchy. It is shown that M\"obius symmetry transformation for the singular manifold equation leads to continuous or…
In this paper we study the controllability of the Keller-Segel system approximating its parabolic-elliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the parabolic-elliptic…
In the present paper we extend the multiparameter coupling constant metamorphosis, also known as the generalized St\"ackel transform, from Hamiltonian dynamical systems to general finite-dimensional dynamical systems and ODEs. This…
Recently we proposed a generic construction of the additional integrals of motion for the St\"ackel systems applying addition theorems to the angle variables. In this note we show some trivial examples associated with angle variables for…
We consider the dispersion managed nonlinear Schr\"dinger equations with quintic and cubic nonlinearities in one and two dimensions, respectively. We prove the global well-posedness and scattering in $L_x^2$ for small initial data employing…
This paper aims to construct structure-preserving numerical schemes for multi-dimensional space fractional Klein-Gordon-Schr\"{o}dinger equation, which are based on the newly developed partitioned averaged vector field methods. First, we…
The aim of the article to clarify the status of Shapiro plane wave solutions of the Schr\"odinger's equation in the frames of the well-known general method of separation of variables. To solve this task, we use the well-known cylindrical…
How does the spectrum of a Schr\"odinger operator vary if the corresponding geometry and dynamics change? Is it possible to define approximations of the spectrum of such operators by defining approximations of the underlying structures? In…
The Mesoscopic Mechanics (MeM), which has been introduced in a previous paper, is relevant to the electron gas confined to two spatial dimensions. It predicts a special way of collective response of correlated electrons to the external…
A known general class of superintegrable systems on 2D spaces of constant curvature can be defined by potentials separating in (geodesic) polar coordinates. The radial parts of these potentials correspond either to an isotropic harmonic…
A generalisation of the classical Calogero-Moser model obtained by coupling it to the Gaudin model is considered. The recently found classical dynamical r-matrix [E. Billey, J. Avan and O. Babelon, PAR LPTHE 93-55] for the…
We apply the spectral element method to the determination of scattering and bound states of the multichannel Schr\"odinger equation. In our approach the reaction coordinate is discretized on a grid of points whereas the internal coordinates…
The paper contains a brief description of a simplified version of A. Sobolev's proof of absolute continuity of spectra of periodic magnetic Schr\"{o}dinger operators. This approach is applicable to all periodic elliptic operators known to…
It is shown that several Hamiltonian systems possessing dynamical or hidden symmetries can be realized within the framework of Nambu's generalized mechanics. Among such systems are the SU(n)-isotropic harmonic oscillator and the…
We present a spectral method for solving elliptic equations which arise in general relativity, namely three-dimensional scalar Poisson equations, as well as generalized vectorial Poisson equations of the type $\Delta \vec{N} + \lambda…
A novel strategy is proposed for the coupling of field and circuit equations when modeling power devices in the low-frequency regime. The resulting systems of differential-algebraic equations have a particular geometric structure which…
In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem…
A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to…
This work considers numerical methods for the time-dependent Schr\"{o}dinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that…
A nonperturbative procedure of solving the time-dependent Schr\"odinger equation, called the multi-projection approach or phase dynamics of quantum mechanics, is derived and illustrated. In addition to introducing a method with that…