Twisted hierarchies associated with the generalized sine-Gordon equation

Twisted U-and twisted U/K-hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted O(J,J)/O(J)xO(J)-hierarchies are among the most important classes of twisted hierarchies. In this paper, we derive explicit interesting first and higher flows of twisted O(J,J)/O(J)xO(J)-hierarchies, justify that the one-dimensional systems of twisted O(J,J)/O(J)xO(J)-hierarchies for J= Iq,n-q(1 <= q <= n-1), called the generalized sinh-Gordon equations, are the Gauss-Codazzi equations for n-dimensional timelike submanifolds with constant sectional curvature 1 and index q in pseudo-Euclidean (2n - 1)-dimensional space R-2q-1(2n-1) with index 2q - 1. Furthermore, a unified treatment of the inverse scattering theory for twisted O(J,J)/O(J)xO(J)-hierarchies is provided. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3633526]