Bäcklund autotransformation for the equationu xt=eu−e−2u

The system of differential relations that arises in connection with the Bullough-Dodd-Zhiber-Shabat equationu _xt=e^u–e^–2u is considered. The consistency of this system is established, and it is shown that the system realizes a Bäcklund autotransformation for the equationu _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 equationu _xt=e^u–e^–2u, is proposed.Bashkir State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 1, pp. 146–159, April, 1993.