The Lotka-Volterra Equations and the QR Algorithm.

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  • Nagai Atsushi
    Department of Mathematical Sciences, University of Tokyo, Komaba 3–8–1, Meguro–ku, Tokyo 153
  • Satsuma Junkichi
    Department of Mathematical Sciences, University of Tokyo, Komaba 3–8–1, Meguro–ku, Tokyo 153

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  • Lotka Volterra Equations and the QR Alg

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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 dNk/dt=Nk {Nk+1(Nk+Nk+1+Nk+2) -Nk-1(Nk-2+Nk-1+Nk)}, 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.

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