The Lotka-Volterra Equations and the QR Algorithm

Abstract

It is shown that a hierarchy of the Lotka-Volterra equations is generated from the QR algorithm to find eigenvalues of a given matrix. One of 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 with other four species. The relation between this hierarchy and the Toda lattice hierarchy is discussed. Moreover, the structure of soliton solutions is studied by means of the bilinear formalism.