Related papers: A new solvable many-body problem of goldfish type

The 2-body problem on the sphere and hyperbolic space are both real forms of holomorphic Hamiltonian systems defined on the complex sphere. This admits a natural description in terms of biquaternions and allows us to address questions…

In this paper we define a small variation of the Taylor method and a formula for the global error of this new numerical method that allows us to keep track of the round-off error and does not require previous knowledge of the exact…

In this paper, we consider periodic solutions of the $n$-body problem that satisfy symmetry constraints, expressed through invariance under finite group actions. We focus on their stability properties and present algorithms specifically…

In this paper we prove existence and uniqueness of solutions to a nonlocal parabolic problem which generalizes the electric heating problem of a conducting body.

Examples are given of solutions of the planar N-body problem which remain the same for at least two systems of masses with the same sum and same center of mass. The least value of N achieved up to now with this property is 474, a number…

We prove that fundamental groups of orientable (geometrizable) 3-manifolds have a solvable conjugacy problem.

We show that the equations underlying the $GW$ approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact,…

We consider the ternary Goldbach problem with two prime variables of the form $k^2+m^2+1$ and find an asymptotic formula for the number of its solutions.

There exist methods to reformulate in an exact way the many-body problem of interacting bosons in terms of the stochastic evolution of single particle wave functions. For one such reformulation, the so-called simple Fock scheme, we present…

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…

The goal of the paper is to give characterization of closed connected manifolds which admit a global multisympletic 3-form of some algebraic type. A generic type of such 3-form is equivalent to a G2-structure. This is the most interesting…

Here a mixed problem for a nonlinear hyperbolic equation with Neumann boundary value condition is investigated, and a priori estimations for the possible solutions of the considered problem are obtained. These results demonstrate that any…

In this article we describe recent progress in the computational many-body theory of metal surfaces, and focus on current techniques beyond the local-density approximation of density-functional theory. We overview various applications to…

An approach is developed to find approximate solutions to the classical Newtonian problem of N bodies. Sets of N gravitating bodies having spherically symmetric mass distributions, small angular velocities (< 1 rad/s) and bounded position…

In this paper we consider a class of Burgers equation. We propose a new method of investigation for existence of classical solutions.

This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable…

General properties of the three-body problem in a model of modified dynamics are investigated. It is shown that the three-body problem in this model shares some characters with the similar problem in Newtonian dynamics. Moreover, the planar…

Self-similar solutions of the equations for the Burgers hierarchy are presented.

The paper deals with continuous solutions of a Schilling's problem.

We construct a family of quasi-solvable quantum many-body systems by an algebraic method. The models contain up to two-body interactions and have permutation symmetry. We classify these models under the consideration of invariance property.…