Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
Integrable reductions of the Bogoyavlenskij-Itoh Lotka-Volterra systems
Given a constant skew-symmetric matrix A, it is a difficult open problem whether the associated Lotka-Volterra system is integrable or not. We solve this problem in a special case when A is a Toeplitz matrix where all off-diagonal entries are plus or minus one. In this case, the associated Lotka-Volterra …