
TY  - JOUR
A1  - Jeffery, EA 
T1  - New Classical Solutions to F4 Theory
JF  - Australian Journal of Physics
JO  - Aust. J.  Phys.
Y1  - 1981
VL  - 34
IS  - 2
SP  - 113
EP  - 120
KW  - 
UR  - https://doi.org/10.1071/PH810113 
N2  - The partial differential equation 02rf>+m2c/>+Ac/>3 = 0 (where 0 2 = 0;-\72) is converted to the ordinary differential equation 2¢>/du2 + (Nlu)d¢>ldu +m2c/> +).¢>3 = O. In this conversion, 02U and (OU)2 are assumed to depend only on u, where u is a  Fnction of x,y, Z, t, and further, Nlu is the normal curvature of the hypersurface u = constant. In order to solve for u, the analogous Euclidean 4-space problem with 0 2 = 0; +\72 is examined initially. The only possible values of N are then 0, 1, 2, 3 corresponding to hypersurfaces that are a hyperplane, a hypercylinder (one curved face), a hypercylinder (two curved faces) and a ypersphererespectively. These hypersurfaces are transformed to Minkowski space via xk ~ ixk , k = 1,2,3. Then by solving the ordinary differential equation new solutions to the original partial differential equation are found, one of which has a closed form. 
ER  -

