ISOGROUPS AND EXACT-SOLUTIONS FOR SOME KLEIN-GORDON AND LIOUVILLE-TYPE EQUATIONS IN N-DIMENSIONAL EUCLIDEAN-SPACE

metry variables and the isovector approach, the generalized forms of nonlinear Klein-Gordon and Liouville equations in n-dimensional Euclidean space are analyzed herein. The construction of the components of the associated isovector field via transport property under Lie derivative leads to orbital equations whose solutions yield invariant groups of transformations. These invariant groups reduce the equations under consideration to nonlinear ordinary differential equations (ODEs) involving arbitrary functions of the new dependent and independent variables. Finally, exact solutions of these resulting ODEs are tabulated for different forms of these arbitrary functions. Beside recovering the available results for particular forms of the said arbitrary functions involved in the ordinary differential equations, some new exact solutions are reported. (C) 1995 American Institute of Physics.