B\"acklund transformation and the construction of the integrable boundary-value problem for the equation $u_{xx}-u_{tt}=e^u-e^{-2u}$

Abstract

B\"acklund transformation for the Bullough-Dodd-Jiber-Shabat equation $u_{xx}-u_{tt}=e^u-e^{-2u}$ is found. The construction of integrable boundary condition for this equation together with the algebro-geometric solutions satisfying it are suggested.