Nonlinear standing and rotating waves on the sphere (Q1586118)

The authors of this paper establish the existence of time-periodic solutions of semi-linear wave equations on the unit sphere in \(R^3\). The authors get the branches of small-amplitude solutions and the precise spatio-temporal patterns of solutions by using the delicate methods of bifurcation theory and the well-known group-theoretic ideas. Moreover the authors prove the existence of global solution branches in sense of P. Rabinowitz.