Abstract <p> A method for solving the double and triple sine-Gordon equations with first derivatives is presented. The search for solutions is similar to the search for functionally invariant solutions of the multidimensional wave equation. The solvability of the resulting system of equations is analyzed. The solution of the double sine-Gordon equation is obtained in explicit form by inverting the elliptic integral. The solution of the triple sine-Gordon equation requires inversion of the ultra-elliptic integral in the general case. </p>