E.L. Aero, A.N. Bulygin, Yu.V. Pavlov
Exact analytical solutions of (3+1)-dimensional generalized sine-Gordon equation are obtained that in distinction from classical equation contain additional partial derivatives of first order on variables . Solutions contain arbitrary function of ansatz , which must satisfy to some system of algebraic equations. Solutions found have an important property, namely, for the function a principle of superposition is valid. Proposed approach is applicable to the integration of sinh-Gordon equation and admits the natural generalization on the case of integration of given types of equations in the space of arbitrary dimension.