A Bäcklund Transformation of a Kind of Nonlinear Wave Equation

Applying the method of canonical, transformation, we studied the nonlinear wave equation φ_xx - φ_tt = dF ( φ ) /dφ . A Bäcklund transformation (BT) of this equation is obtained. Combining BT of this equation with the well-known BT of sine-Gordon equation (SGE), a formula of nonlinear superposition which contains some arbitrary functions of x and t has been established. This formula leads to a kind of general solution of SGE through its some known solutions. The general soliton solutions and their properties are simply discussed.