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

In this paper, we constuct the multi-point blowup solutions of self-similar type for the inviscid Burgers equation. The shape and blowup dynamics are precisely described. Moreover, the solutions we construct are stable under small…

In this paper we are concerned with some $p$-Kirchhoff type problems involving sign-changing weight functions. We prove the existence of multiple positive solutions of the problem via the Nehari manifold approach.

A new type of multi-soliton solution to the ultradiscrete Toda equation is proposed. The solution can be transformed into another expression of solution in a perturbation form. A direct proof of the solution is also given.

Possible solution of problem of sovereign debts is suggested. At the current moment this solution still can be provided only by methods of the world monetary policy.

An introduction to Joyal's theory of combinatorial species is given and through it an alternative view of Rota's twelvefold way emerges.

Number of results in number theory have been developed using a new method. The Goldbach binary conjecture in strengthened formulation have been among them.

This paper introduces a new difference scheme to the difference equations for N-body type problems. To find the non-collision periodic solutions and generalized periodic solutions in multi-radial symmetric constraint for the N-body type…

We find integrals of motion for the recently introduced deformed Ruijsenaars-Schneider many-body system which is the dynamical system for poles of elliptic solutions to the Toda lattice with constraint of type B. Our method is based on the…

A brief introduction and overview is given of the complexity that is possible and the challenges its study poses in many-body systems in which spatial dimension is irrelevant and naively one might have expected trivial behaviour.

We present several examples of quasi-exactly solvable $N$-body problems in one, two and higher dimensions. We study various aspects of these problems in some detail. In particular, we show that in some of these examples the corresponding…

We study a 2+2 body problem introduced in a previous paper as the circular double Sitnikov problem. Since the secondary bodies are moving on the same perpendicular line where evolve the primaries, almost every solution is a collision orbit.…

This communication records some observations made in the course of studying one-relator groups from the point of view of residual solvability. As a contribution to clas- sification efforts we single out some relator types that render the…

This paper collects polynomial Diophantine equations that are simple to state but apparently difficult to solve.

The classical solvability of the initial-boundary problem for the Davey-Stewartson-II type system of equations is proved.

The existence and uniqueness of a solution to a generalized Blasius equation with asymptotic boundary conditions are proved. A new numerical approximation method is proposed.

We introduce an analytically solvable model for a fragmented object that, despite of a low degree of randomness and of the extreme simplicity of the breaking process, displays non self-averaging effects in its thermodynamic limit.

A novel technique for solving some head-on collisions of plane homogeneous light-like signals in Einstein-Maxwell theory is described. The technique is a by-product of a re-examination of the fundamental Bell-Szekeres solution in this field…

This paper is concerned with complex macroscopic behaviour arising in many-body systems through the combinations of competitive interactions and disorder, even with simple ingredients at the microscopic level. It attempts to indicate and…

We consider inverse problems for non-linear hyperbolic and elliptic equations and give an introduction to the method based on the multiple linearization, or on the construction of artificial sources, to solve these problems. The method is…

This article introduces the "Goldilocks model" for a few repulsively interacting particles trapped in a one-dimensional harmonic well and provides exact solutions for the three-particle case. The Goldilocks model shares features with two…