Gianni Arioli, Hans Koch
Periodic and quasiperiodic waves on the sphere
(3021K, pdf)

ABSTRACT.  We construct periodic and quasiperiodic solutions 
for the nonlinear plate equation on the unit sphere in R^3. 
Periodic solutions for the nonlinear wave equation are constructed as well. 
The methods do not involve small parameters. 
In the case of a cubic nonlinear term, our approach is computer-assisted 
and thus yields detailed information about each solution. 
For nonlinearities that are in some sense close to linear, 
weak solutions are obtained by a variational method.