Related papers: Noncollision Singularities in a Planar Four-body P…
We investigate the correlations between different bipartitions of an exactly solvable one-dimensional many-body Moshinsky model consisting of Nn "nuclei" and Ne "electrons". We study the dependence of entanglement on the inter-particle…
Exponential small splitting of separatrices in the singular perturbation theory leads generally to nonvanishing oscillations near a saddle--center point and to nonexistence of a true homoclinic orbit. It was conjectured long ago that the…
A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…
We obtain the local existence and uniqueness for a system describing interaction of an incompressible inviscid fluid, modeled by the Euler equations, and an elastic plate, represented by the fourth-order hyperbolic PDE. We provide a~priori…
Moeckel (1990), Moeckel and Sim\'o (1995) proved that, while continuously changing the masses, a 946-body planar central configuration bifurcates into a spatial central configuration. We show that this kind of bifurcation does not occur…
We are developing a covariant model for all mesons that can be described as quark-antiquark bound states in the framework of the Covariant Spectator Theory (CST) in Minkowski space. The kernel of the bound-state equation contains a…
We study the equal-mass classical three rotor problem, a variant of the three body problem of celestial mechanics. The quantum $N$-rotor problem has been used to model chains of coupled Josephson junctions and also arises via a partial…
The scalar three-body Bethe-Salpeter equation, with zero-range interaction, is solved in Minkowski space by direct integration of the four-dimensional integral equation. The singularities appearing in the propagators are treated properly by…
Anti-self-dual metrics in the $(++--)$ signature which admit a covariantly constant real spinor are studied. It is shown that finding such metrics reduces to solving a fourth order integrable PDE, and some examples are given. The…
This study presents a general alternative scheme of the procedure and necessary conditions for solving the $n$-body problem. The presented solution is not a solution of the classical problem, where the initial conditions of positions and…
We study spacetime singularities in a general five-dimensional braneworld with curved branes satisfying four-dimensional maximal symmetry. The bulk is supported by an analog of perfect fluid with the time replaced by the extra coordinate.…
In this paper, we further investigate the planar Newtonian three-body problem with a focus on collinear configurations, where either the three bodies or their velocities are aligned. We provide an independent proof of Montgomery's result,…
The paper deals with the study of a satellite attracted by n primary bodies, which form a relative equilibrium. We use orthogonal degree to prove global bifurcation of planar and spatial periodic solutions from the equilibria of the…
We give a simple proof of our previous result with V. Zharnitsky that the set of period 4 orbits in planar outer billiard with piecewise smooth convex boundary has empty interior, provided that no four corners of the boundary form a…
We study the solutions of the second Painlev\'e equation in the space of initial conditions first constructed by Okamoto, in the limit as the independent variable, x, goes to infinity. Simultaneously, we study solutions of the related…
In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii's fixed point theorem on cones, sufficient conditions for the…
By extending previous analysis of the authors, a systematic study of the singularity structure and possible asymptotic behaviors of five-dimensional braneworld solutions is performed in the case where the bulk is a mixture of an analog of…
A degenerate fourth-order parabolic equation modeling condensation phenomena related to Bose-Einstein particles is analyzed. The model is a Fokker-Planck-type approximation of the Boltzmann-Nordheim equation, only keeping the leading order…
We show that the most general scalar-tensor theory of gravity up to four derivatives in $3+1$ dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We…
In this work we survey four classic problems: Borsuk's partition problem, Tarski's plank problem, the Kneser--Poulsen problem on the monotonicity of the union of balls under a contraction of their centers, and the Hadwiger--Levi problem on…