BACKLUND AUTOTRANSFORMATION FOR THE EQUATION U(XT)=E(U)-E(-2U)

The system of differential relations that arises in connection with the Bullough-Dodd-Zhiber-Shabat equation u(xt)=e(u)-e(-2u) is considered. The consistency of this system is established, and it is shown that the system realizes a Backlund autotransformation for the equation u(xt)=e(u)-e(-2u). The associated three-dimensional dynamical systems, which are compatible on a two-dimensional invariant submanifold, are investigated, and a construction of their general solution, which gives the explicit form of the three-parameter soliton for the equation u(xt)=e(u)-e(-2u), is proposed.