THE LOTKA-VOLTERRA EQUATIONS AND THE QR ALGORITHM

It is shown that a hierarchy of the Lotka-Volterra equations is genera ted from the QR algorithm to find eigenvalues of a given matrix. One o f the equations in the hierarchy is given by dN(k)/dt=N-k {N-k+1(N-k+N -k+1+N-k+2)-N-k-1 (N-k-2+N-k-1+N-k)}, in which one species interacts w ith other four species. The relation between this hierarchy and the To da lattice hierarchy is discussed. Moreover, the structure of soliton solutions is studied by means of the bilinear formalism.