Integrability and a Solution for the One-Dimensional N-Particle System with Inversely Quadratic Pair Potentials

Abstract

Integrals of Hénon’s type are given for the system with inversely quadratic pair potentials. The explicit time dependence of solution are given for the repulsive case. A little extension and modification make it possible to have a solution for the system with quadratic and inversely quadratic pair potentials.