Some remarks on complex Hamiltonian systems

The analyticity property of the one-dimensional complex Hamiltonian system H(x,p) = H-1(x(1), x(2) , p(1), p(2)) + iH(2)(x(1), x(2), p(1), p(2)) with p = p(1) + ix(2). x = x(1) + ip(2) is exploited to obtain a new class of the corresponding two-dimensional integrable Hamiltonian systems where H-1 acts as a new Hamiltonian and H-2 is a second integral of motion. Also a possible connection between H-1 and H-2 is sought in terms of an auto-Backlund transformation. (C) 2000 Elsevier Science B.V. All rights reserved.