A novel solvable many-body problem with elliptic interactions
Résumé
The Hamiltonian system characterized by the Newtonian equations of motion
x¨n=∑Nm=1,m≠nx˙nx˙mw(xn−xm), w(x)=2 ζ(x)+λx
, where ζ(x)≡ζ(x|w,w′) is the Weierstrass zeta function and λ is an arbitrary constant, is solvable provided there holds the single constraint (on the initial data) ∑Nn=1x˙n(t)=∑Nn=1x˙n(0)=0.