Functionally invariant solutions of triple sine-Gordon equation

Functionally invariant solutions U(x, y, z, t) of triple sine-Gordon equation with constant amplitudes are received. Solutions have the form of composition of two functions U[W(x, y, z, t)]. Function W(x, y, z, t) satisfies two equations simultaneously: the wave equation and the eikonal-type equation. Functionally invariant solutions of these equations are found. Solutions contain an arbitrary function F(a). Ansatz a(x, y, z, t) may be found from the algebraic equation linear on independent variables (x, y, z, t). The coefficients of the algebraic equation are arbitrary functions of a. Ansatz is defined ambiguously. Simple expressions for the ansatz a(x, y, z, t) are found. Dependence U from W is defined by the solution of the nonlinear ordinary differential equation of the second order. Analytic properties of the obtained solutions are discussed.