MULTIDIMENSIONAL SOLUTIONS OF THE NONLINEAR KLEIN-GORDON EQUATION

The nonlinear Klein-Gordon equation in higher dimensions can be reduced to either parabolic, hyperbolic or elliptic nonlinear equations in two independent variables. Some special types of solutions of these reduction equations are presented. The solutions of the reduced parabolic equation possesses two arbitrary functions of x + t. The generalized collapsons and a special type of pulse-like solitary wave solutions which possesses finite total energy in the (2 + 1 )-dimensional case are just special examples of this type of solutions. Some special solutions of the reduced hyperbolic and elliptic equations are the kink-antikink-like, breather-like and kink-wave-like solutions.